I also want to respond to some of the common arguments that people have made for having a new protagonist.
1) The next story might not be about Solas and the veil.
Considering that Solas is going to bring down the veil in a few years, there hardly seems to be enough time to squeeze in some other major event in between. Besides, the Inquisitor has already began his/her mission to stop Solas as seen by the last cut scene in Trespasser. Also, there is something very jarring about mucking around with Tevinter vs. Qunari or whatever while you know that there is impending world destruction. If there is going to be a Qunari vs. Tevinter war or a slave uprising, these should be background conflicts instead of the primary event. If those conflicts exist, I imagine that they would be treated like the Mage Templar war in DAI.
2) Another PC stopping Solas would further make him understand that the people of modern Thedas are people too.
Unless you were playing assquisitor, Solas is already convinced that the people of modern Thedas are people. He doesn't need another person to tell him that. His dilemma is that for some reason, he believes that bringing down the veil is the only way to "save" his people. The Inquisitor will also probably "save" the modern people over the ancient elves if there were no other option. Neither group is somehow more valuable than the other. It's just a shitty situation that has no good solution as Solas believes. Also, even if you were playing assquisitor or don't care for redeeming Solas, the writers still have the responsibility to account for those who want to redeem him, especially since we were given the option to attempt that.
3) Solas threatens everyone and not just the Inquisitor.
Yes that is true, but the story will likely be less nuanced if Solas confronts a new PC. Weekes wrote the Solas Lavellan romance just to make him seem more sympathetic. Even though some players don't care about Solas or think he's just pure evil/psycho, it is clear that this was not the writer's intention. Solas was likely written as your companion/friend/potential lover/rival in order for you to care about him (whether love or hate) and not just defeat him as some generic big bad. The writers may not have reached every player with this intent, but they reached probably at least half of the player base and it would be irresponsible to get your players attached to a character/relationship and then ignore it in the next game when there is no closure in the current game. One could argue that they could rebuild such a relationship with a new PC, but that's frankly a waste of time considering that they have already spent a whole game doing that. Honestly, I don't want a repeat of the Corypheus situation in which I knew I had to stop him, but could care less about him either way.
4) Finally, I will talk about the dual protagonist option.
I will take this over nothing, but I still feel that it is not as clean as just having the inquisitor be the only PC for the next game. Having the new PC be the main playable character still has all the problems that I noted in the previous paragraphs. I think that if I were playing the new PC most of the time, I would just be thinking about how the Inquisitor will likely have more interesting and emotional reactions to events because of his/her previous knowledge about Solas.