The answer is the absurd some of money it would cost, quite apart from the fact that those VAs may make it impossible to fit the game on one disk. That's just from the technical POV.
Beyond that, there's almost certainly a new protagonist in DA4.
Dude you realize that there were 4 voice options for the Inquisitor this time? 2 female and 2 male. So how would it cost more? You might even add a third voice option for DA4 this is a pretty stupid argument.
Why not have the Warden? Solas doesn't know him so he/ she would fit the bill perfectly. Furthermore 2/3 of the Inquisitiors won't be able to fight anymore because they are either warriors (hard to hold a shield or swing a two-handed-weapon with one arm) or rogues (hard to use dual daggers, draw a bow or redraw a crossbow with one arm) and going by the lore so far it would be pretty hard for a mage too (how will you conjure anything with one hand while holding a stick?). So he/she is pretty much out and given that the rest of your mates get older and have stuff to do and are known to Solas intimately it would make sense to have the Warden as a protagonist.
Leliana/Cassandra/Vivienne is Divine so they are out either way.
Cullen must be the wrong side of 40 by then and was never more than an advisor and it wouldn't make much sense for him to be anything else.
Josie is back in Antiva.
Cassandra will probably take Cullen's place as the leader of your forces.
Varric is Viscount of Kirkwall and so he won't be able to just **** off and go help you, if he does, he is well past 40 by then so chances are he will be your new spymaster.
Dorian is deeply involved in a struggle in Tevinter and will most likely not **** off because he would leave all of his allies in harms way and lose massive influence in the imperium and you will need him when you are actually active in Tevinter.
Sera will come back but Solas knows her well so that would defeat the point.
Blackwall will likely somehow be involved since the Andernfels is near Tevinter but in the end he is a Warden now so no chance he will join you again.
Vivienne is the Grand Enchanter or Divine so no chance there.
Cole: Maybe but again... Spirit and all that against a powerful mage? Don't see it.
The Iron Bull: Intimately known so not really furthermore probably more involved in protecting Dorian from Tevinter assassins in the Civil War.
Dagna: Might become the first Dwarfen Mage... would be cool.
Let's look at older companions:
Isabella: definitely a possibility.
Merrill: pretty sure she will return maybe even alongside Hawke as a party member.
Fenris: Tevinter? Hell yeah he will be back.
Aveline: same as Varric, Vivienne etc.
Carver/Bethany: see Blackwall if they were turned into a warden.
Anders: No Chance.
Sebastian: See Varric etc.
Wynne: Most likely dead.
Sten: Doubt it... Qun and all that.
Zevran: Always on the run, always in hiding... no chance that he will expose himself like that again.
Morrigan: Maybe but I doubt it because she wants to hide from Flemmeth.
Oghren: Probably a Warden so again: Blackwall and all.
Alistair: Either a drunk, king or still warden so... Blackwall, Leliana/Cassandra/Vieviene/Varric or just gone.
Shale: Possible and likely as a squishy Dwarf because she went to Tevinter to become a real dwarfette again.
So basically apart from 2-3 people there won't be any return into the active parties. Cassandra will probably take Cullen's place and you will need a new Ambassador/Contact to the nobility and a new Spymaster (might actually be Sera). I doubt Leliana will be intimately involved because I think her becoming Divine will become canon. She is the only one to really change the chantry and it feels like that this is the situation the south will be in because in the end the games are about changing things for the better and Leliana is the only one doing that and her chantry is the only one that would have any appeal to the rogue elfes. Your inquisitior will most likely just be a figurehead because of his disability.
I think the HoF would be amazing simply because the story is less Grey Wardeny but you will need one because of Weißhaupt. I think you might get Hawke and Merrill in some capacity, Scout Harding, Dagna and Shale.
Anyhow... I don't get what is so terrible about a character over whom you had basically total control instead of some cheesy dude or dudette who sputed some cheesy lines. I think many have a really deep connection to their warden just because of the voicelessness in DA:O.