Logic does not follow. For one, Arabic script is not any more complicated than Latin script, so your entire case collapses in your first sentence.
Not quite. The Ottoman variation of the Perso-Arabic script was actually pretty complex, seeing as it borrowed loanwords from all over the place without bothering to making them fit into Turkish pronunciation (much like how English orthography operates) and largely adopted the form that was used originally for Persian with some minor changes. On top of that, vowel diacritics were often omitted in Ottoman writing - which works fine in Arabic, but in a language like Turkish where vowels are important it actually creates massive issues since even from context it's hard to disambiguate words written in this manner. By this point, it should be noted that there were some attempts to reform the Ottoman script to make it more "phonetic" (= phonemic), but all of them were massively opposed by conservative forces who did not want to break with tradition as inherited from Arabic (keeping in mind that even the Arabic component in Ottoman Turkish was complex and similar to the different types of readings of Chinese characters in Written Japanese, which added more needless complications). So reformers looked around for alternative solutions, even briefly experimenting with Armenian script for a bit, before settling on the Latin script. So in this case, the idea of Latinization was nothing new; what was new were the exact details.