Sedeprivationism is intellectually rigorous, and a worthy effort, but I don't think it answers the great difficulties that simple sedevacantism raises, and which it was devised to resolve.
Sedeprivationists would need to cite a traditional source justifying their division of authority or jurisdiction into a composite having matter and form, because typically authority is not divided in such a way. To possess an office is to possess the authority or jurisdiction attached to it, there is nothing else beside it to possess. He who does not possess authority over a particular flock, who does not stand in a habitual relationship over them, does not possess the office in any way, not even materially.
Jurisdiction is in its essence, as all canonists and theologians explain, a relationship between a superior who rules and a subject, or flock, who is ruled, the one standing in a real metaphysical relationship over the other within the Mystical Body. But if this is lacking, in what sense precisely is the material occupant still an occupant of the see?
It is said the Popes retain only the material element of the Papacy, which is the title and designation, but lack the formal component, which is the authority and jurisdiction, a distinction that was not traditionally made.
Granting this for now, for argument's sake. Then, it is claimed that these "material Popes" can designate others, such as electors and even bishop-designates.
So, the two questions of the greatest import are - can the "material Pope" really designate Cardinals, can he appoint Ordinaries to other sees of authority?
Fr. (later Bp.) Lauriers was the principal expositor of this thesis, but its leading exponent today is Bp. Sanborn - this is what he writes,
"This right of designating, which is found in Paul VI or in John Paul II does not constitute them as popes, because they lack authority or the right of making law. Therefore they are not popes except materially. They can, nevertheless, designate electors and even bishops for the purpose of succeeding to sees of authority"
This thesis is very complicated and therefore its refutation will correspondingly be such as well - the brief answer is this - the traditional doctrine is this, when a Pope appoints a bishop, it is his Papal power, the universal jurisdiction that he possesses in act, that effects the transmission of particular jurisdiction onto the bishop. But if sedeprivationists deny the Pope his universal jurisdiction, then the bishops he appoints will not have particular jurisdiction, for the cause is lacking, the effect cannot be realized. The bishops he appoints, as some sedeprivationists concede, will also just be mere material occupants of their episcopal sees. But in this case formal Apostolic succession will cease, because formal Apostolic succession requires the transmission of the ordinary power of jurisdiction.
Will a Pope designate be able to designate Cardinals? It may be doubted. For Cardinals receive the right of election because, as their name suggests, they are incardinated into the Roman Church, enabling the Petrine succession to continue. Now, incardination is an act where one cleric is transferred from the jurisdiction of one bishop to that of another (see
http://www.newadvent.org/cathen/07704a.htm ), to henceforth stand in a habitual relationship to the bishop of the place where he is newly incardinated, in this case the diocese of Rome. But if this habitual jurisdiction and it precisely is lacking, how is the act of incardination to be effected? In this case, the Cardinal will not then receive the power of designation, because he will not be incardinated into the Roman Church, where the power prinicipally resides.
These, briefly, are some of the critiques non-sedeprivationists have made of the thesis. Undoubtedly it is a serious effort to make sense of a difficult situation, but ultimately an unsuccessful one.