The problem with Zoroastrianism is that it shares many of the same concepts with Islam, but lacks some of the important strengths.
The universe is in a state of struggle between good and evil. Each of us has to make choices, with good obviously being the preferred option. Speaking the truth is central. These concepts are key in both Zoroastrianism and Islam.
The difference is that Islam was more community focused and much less elitist. For example, only priests were allowed in temples whereas in Islam anyone can pray anywhere any time. Anybody could become Muslim, especially after the Abbasid revolution in 750 which abolished the requirement to find an existing Muslim to sponsor you. (It was originally necessary to join one of the recognised Arab tribes).
Furthermore, it was relatively easy for Zoroastrians and Christians to convert to Islam as they already share many of the same core beliefs. For example Ahura Mazda (force of good) becomes Allah, while Ahriman (force of evil) becomes Satan the devil. And the focus on "good thoughts, good words, good actions" in Zoroastrianism is easily translated into Islam too, which expresses the same values repeatedly accompanied by many examples and stories of kind acts, forgiveness, charity and so on.
Many of these factors listed above are found in Christianity too, making it easy for Zoroastrians to convert to Christianity as well.
Zoroastrianism had become obsolete, which is why it died out. Aspects of it such as the choice between good and evil and the emphasis on speaking the truth survive in Islam (and to some extent Christianity) to this day.
The problem with this concept is that they are not that much alike. Zoroastrianism was for one dualist and also a religion based upon a massive amount of traditions, rural culture, state power and the lineage of the people. It's rapid fall to Islam is quite odd, I personally do not know why this occurred as it did and I doubt there is a concise answer for why Iran fell to Islam so profoundly, whereas the traditional faiths of Hindustan continually resisted. Out of all the lands that dar al-Islam conquered, Iran is one for the most easily Islamized and most rapidly done so. By the time of al-Tabari, already Islam was profoundly dominant and Zoroastrians were barely mentioned, with great shaykh already arising in Iran by the Abbasid period. To compare, let me mention areas conquered by dar al-Islam and briefly mention its conversion.
Arabia: Rapidly brought to Islam of some form, however, quickly they veered from Islam as held by the Caliphate. In the earliest days of the Caliphate, during the reign of Uthman ibn Affan, scholars already point to a syncretic nature of some peoples. Such as the Khawarij who killed Uthman ibn Affan or the origins of the primordial Shi'i movement which would come to be a completely separate religion in most ways. By the time of the Abbasid hegemony, various conglomerates of Shi'i maintained pagan traditions and or morphed with older religions, such as Manichaeism or general traditional faiths of the peoples. In 810-885, Arabs on the east coast were in a constant state of rebellion, claiming the ways of the Imamiyyah and later other ideals that came not form the Islam pronounced by the ulema or the khilafah. Not to mention, into modern times, there were Arabs in the Nejd who still practiced a form of Arab originated Kharijism or paganism as reported from the books of the time that reported the worship of trees, rocks and what have you by the inhabitants of the Nejd.
Iraq: Never truly completed in a satisfactory way. Ghulatti Shi'i were predominant in southern Iraq fro centuries, with the centers of the Shi'i Imamiyyah centered within Iraqi ctiies of Najaf-Karabala-Kufa, that was reported to be the land in which arose the Shi'i. Further, the northern sections of Iraq for the majority of the Islamic period, remained Christian and in many areas, Yazidi or traditional faiths. There is also the case of the Mandaens in Southern Iraq who despite their small size, kept greater retention than Zoroastrians within Iraq. Manichaens had terrible repression under the Abbasid period, perhaps due to their visibility, which other groups were experts at. When I say visibility, the key was either having an extremely strong tradition that made a religion resistant to rapid Islamic dawah (missionary activities) or to have a formula for concealment that allowed your group to sustain itself despite the flood of Islam.
-Jews, strong tradition and often had valued skills for the Abbasid state. Their status in urban areas also gave itself to blending with local populaces.
-Christians, strong tradition, culture that accepted martyrs without surrender, very literate in urban areas and thus useful, large amounts of taxable land and income.
-Manichaens, leaders were often literate so useful, however, they were very visible due to their ornate religious texts, sophisticated religious hierarchy (that led to poorly learned followers who were often willing to convert to avoid persecution), Manichaens also had little means to mix with the Muslim as they did in China due to a lack of similarity regarding Muhammad and the lack of images within Islam.
-Mandaens, extremely strong tradition and culture around strict adherence, secrecy and communal duty. The Mandaens also by their secrecy were so mysterious, that the Muslim likely never fully realized their actual ideas, that equated to an even more syncretic religion than many of those found in Iraq. Unlike the Manichaens, their strict communal mentality made ostracism for leaving the community and honor killings common place for converts or out of faith marriage, the followers of Mani conversely were nearly without culture and most examples in Islamic literature we have of them were that of scholars and libertine men in Baghdad.
-Yazidi, shadowy and mysterious traditional faith conglomerations in the north who were fiercely rural and communal. Such is extremely adverse to conversion.
-etc, etc ,etc,,,
However after mentioning those, the various forms of Shi'i were perhaps the most perfect form of resisting religious change from the state mandated religion of the Islamic world. The concepts of secrecy (fiqh al-Hiyal) and the infamous taqiyyah made it extremely difficult for the ruling authorities to know the Shi'i even existed in a region until they rebelled or made some other movement which alarmed the authorities. The taqqiyyah also when at the person to person level gives no room for the missionary to even begin to persuade the Shi'i of the day, for the one within taqiyyah will simply agree to what you say and send you on your way, whilst he denied everything you said as he was given the ideals from a young age to resist the followers of Abu Bakr, Umar, Uthman and Ayesha and was versed in cursing them constantly. The taqiyyah also when spread outward, allows an entire village to portray themselves as what the authorities wish whilst maintaining their practices behind closed doors, this type of concealment is nearly impossible to completely change across a region. Then as soon as the authorities had left the Shi'i alone, suddenly a revolt erupts. Various Zoroastrian revolts numbered as a whole, less than 10, compared to the Shi'i, this is negligible, who rebelled against various Islamic states countless numbers, so much so, that I would have to consult many books just to enumerate the number of revolts. Then after all this, movements of relatively small Shi'i adherents were able to conquer vast lands formerly held by the mandated Islam and convert these lands to the Shi'i form and then wage wholescale war against the Sunni. Examples of this are profound, the Fatimid, Safavid and the various Shi'i tribal states of the Yemeni interior.
In similar fashion to the Shi'i, was that of the Khawarij, who practiced the related form of Hiyal, known as Kitman or offensive secrecy. Kitman itself forwarded itself to the spreading forth into Islamic realms and gaining positions in a region and then turning the society at large into chaos and into revolts, usually involving mass prison breaks, slave revolts, ethnic minorities and simple chaos. Kharijism itself was forwarded to those on the fringes of society and anyone who held hatred against the Khilafah, thus, it was extremely flexible to the times and could be packaged as anything , as long as the goal was the revolt. Khawarij further held the strict views on sin, but did not apply these to their revolutionary who were often criminals, bandits, outlaws and other ruffians whom the thought of religion was surely secondary to loot.
There is also of course the Mu'Tazilah who proliferated through the courts of Baghdad and Samarra. They could easily blend with other Muslim, however, despite essentially taking control over the Abbasid state, their Mihna greatly diminished the power the cliques could enforce and their beliefs were never held by the society at large.
Anyway, back to mentioning regions conversion to Islam.
Iberia: In opposition to Iraq, this area was rapidly converted to Islam if I am not mistaken. The entire southern section of Iberia was Muslim prior to the Reconquista. This is similar to Iran in terms of the rapid conversion, I am not sure as to why this occurred, same for Iran.
This went longer than I wished, but I simply wanted to make the point that Iran converted to Islam relatively easily than other lands and the reasoning for this, is not clear to me.