You are right, the majority of Ulema have rejected Dawlah, however many Ulema support Dawlah now and still do. Baghdadi himself was Ulema for Al Qaeda for instance himself. With that said, many of these Ulema are young and seem to have come from nowhere, and the lack of support from Muhammad al-Maqdisi hurt them. However the illegitimacy of Dawlah is highly complex and is a difficult topic.
The essence of the discussion is Tawheed al-Haakimiyyah and is it independent of Tawheed ar-Raboobiyyah. Tawheed al-Haakimiyyah is that Allah is the sole Hakim (the only judge and arbitrator) and his law (Sharia) is above all, further he and his Deen is the only Tashree (legislator). Tawheed ar-Raboobiyyah is that Allah is the one who has dominion over all and is the giver and taker of life.
The proclamation of Dawlah and Al Qaeda is this: that the Saudi Royal family has betrayed the Ummah and submitted to man made laws and committed Istibdal (changing the law of Allah) and Istihal (making helal what Allah made haram), and are thus Kufr. Those upon the methodology of Osama Bin Laden used to say, that Saudi Arabia has committed Kufr Akbar and are Munafiq because they allowed citizens to take Ribbah (loans on interest) and they allowed Kufr soldiers into the land of the holy Mosque (Mecca). These arguments were refuted by Shaykh Ibn Baz in the late 90s in his series of debates with Osama Bin Laden.
The claim of Dawlah is a bit more complex. They say that Kufr can be committed by the tongue, limbs and the heart (which is legitimate) but the way they apply this ruling against the Saudi regime is ingenious. In Islam, one cannot commit Istibdal and say that another law is above the law of Allah (the Shariah). Dawlah says clearly that by signing the UN charter, which says that the international law is above the law in a nation, is Istibdal with the limbs because the Saudi family accepted it by writing and thus have committed open Kufr Akbar. This is definitely a squirmy situation indeed.
Also there are different terms upon which Khilafah is established and the Ahl ul Hali Wal A'qd are slippery definitions. For instance, Dawlah gives the comparison that if the Mahdi and Isa were establishing Khilafah and if none of the people of influence give the Bayait, does that make their Khilafah invalid? This is again a difficult debate. As well, they combat arguments of the worldwide theory that a Khilafah has to have complete power over the Ummah.
Even if/when Dawlah is defeated, the movement is clear, the ideals of al-Haakimiyyah are becoming more widespread and the debate is only increasing. Interesting topic in my opinion.
It is certanly interesting and complex.
But from the standpoint of the tradition, as I understand it, it is not difficult.
(I am of course referring exclusively to Sunni views here, the only ones that are relevant here).
Your description of doctrinal issues involved in the discussion is absolutely correct, although I do not understand why the Saudi legitimacy is concerned since they never formally claimed the Caliphate. It is true that who exactly the Ahl al-Hall wa al-'aqd are supposed to be. I assume that it's probably safe that most authors had the Ulema, the notables of the community, or both, in mind.
As detailed below, I would take that they are the people whose allegiance to the Caliph guarantees obedience in any given circumstance, but it is a matter of contention.
The sources are pretty clear that Khilafa is defined essentially, given some requirements (for which Ibrahim I may arguably be a poor fit anyway) by the fact of exercising it, that means that means, by being representative of a decent approximation of a consensus of competent Muslims; better said, a Caliph is such, among other things, by his ability to be generally obeyed, and therefore by his broad recognition as a Caliph worth obedience.
This is clearly not the case of Da'ish, although, to be honest, they use the argument in reverse: since the Caliphate is a necessary requirement of religious law (a point which tradition tends to support) whoever refuses obedience to their Caliph, once established, makes themselves apostate in their logic. In this way, they can argue that their Caliphate actually has the obedience/consensus of "real" Muslims. It's circular, real Muslims in this line being the ones who obey their Caliph.
But again, tradition allows for a situation where power in general was seen as legitimate primarily by the fact of exercising itself, so it is not
entirely pulling thing out of thin air in this case.
Not that tradition generally condones declaring disagreements about who sould be Caliph grounds for takfir though.
More generally, talking about "Dawla Islamiyya" in the context of the traditional debate about the Caliphate is ... well, the word I would use is "ungrammatical". "Dawla" means "state" in Modern Standard Arabic, but it means "Dynasty" in the traditional political language (Classical Arabic) in which the discussion was crafted. They had a word for what the Caliph ruled over, but that had never anything to do with the concept of "state": that word was "umma", that is, the community of believers. This in my view betrays a major conceptual disconnect with what the Caliphate used to be and to mean historically.
Of course, as I am not a qualified Muslim interpreter of the tradition, my views on the matter are not religiously autoritative.
