Another thing which bugged me. We know that throughout the series, the holograms had no rights in the Federation. Indeed, they were created to assure certain works and at best, to assist the human beings. So,
1) even if Voyager's EMH, who eventually developed his own personality during the 7 years in DQ, why would the Federation should feel obliging to give him a particular status? We know that the arbitror of the Federation tribunal
consulted just a few weeks or months before the return of Voyager on Earth, was unwilling to declare The Doctor a 'person' at the moment but, he recognized that the matter of holographic rights should soon have to be addressed properly ("Author, Author", 7x20) -> if the Federation works like the Administration and Justice of 20th & 21th centuries - whatever the countries -, our Doctor risks to have to wait for a VERY long time -
if the project is not failed well before for lack of interest or because of its great risk for the Society and/or the security (imagine that all the holograms turn against their creators and get violent like in ??), - to obtain the recognition of his rights like those of others holograms, besides - to exist, to live and be respected like a full individual. If you have doubts, just look at the time which was necessary to impose the civil rights, the right of LBGT, the gender equality, etc...?! And even there, the concern continue!
2) isn't the infamous mobile ermitter of 29th century tech which is proudly wore by the Doctor, in violation of one of the principles of Federation, the temporal prime directive? That Janeway and her crew violated the principle of Prime Directive (standard and temporal) in several occasions to protect themselves could be understood by any commission of inquiry (even if its members will point them out!) :
exceptional circumstances call for exceptional measures BUT after returning home after 7 years, it will be return to the business as usual for Janeway and her crew, including the EMH. And in his case, I'm pretty sure that the Federation won't violate one of its own golden rules to allow him to keep his sentiency.
Likely outcome: the EMH should continue to exist with his current parameters* (it would be stupid to erase all improvements brought, especially as it could be useful) but his freedom of movement will be hindered, deprived of his little case...., until some brilliant engineers, such as B' Elena Torres, create a mobile ermitter of their century.
In both cases quoted, I don't think that the Federation and Starfleet just have that sort of humanity in them, no matter how much bitching Janeway will do to help Seven/Icheb and the Doctor to be inserted! Everybody is not as Janeway with her improved holo Doctor or Doctor Kate Pulaski with Data!
*As bright as he is, he got a temper, our Doctor!

-> remember how Reginald Barclay was treated by his superiors officers and that, is the standard!