I think the primary reason is that Hawke was basically a character with 3 possible personalities, 2 possible voices and 1 possible race, whereas the Warden could have 6 or more voices, backgrounds, and up to 3 races. Also, you're correct that the Warden could also be dead, a king/queen, a Warden-Commander, vanished through the Eluvian, a parent, or simply a wanderer. Hawke is just the champion of Kirkwall who had no choice in what happened after DA2.
Their obsession with bringing Leliana (and Morrigan) back could also be difficult if you romanced her. I suppose it's easier to just make the Warden disappear than put him/her with Leliana.
I believe it's a little concerning for the future because the Warden has basically been dumped due to the sheer difficulty of making him/her a continuing character like Commander Shepard was. Can we expect Bioware to make all our future characters into something less important than they should be based on their standing in Thedas at the end of each game?
How was the Warden dumped? It's been stated numerous time by devs over many years that DAO was the end of the Warden's story (more or less), and future games would involve future protagonists.
Part of that reasoning was perhaps guided by the lack of control they had on the character (all those reasons in your first paragraphs are valid, and very hard to account for), but also because bioware NEVER planned to make DAO into a Mass Effect style storyline, following the same protagonist over several games. This is obvious when you consider they give us the option to perform the Ultimate Sacrifice. Any game where the protagonish can legitimately die in a GOOD ending (as opposed to dying in ME2, which was basically failing the ending) obviously is not planning on keeping that main character around much.
So, no, the Warden was not "dumped": he was never planned to stick around in the first place. Furthermore, I don't agree with the idea that somehow the Warden (or Hawke) is "less important than they should be", because they don't somehow get involved in the Next Big Threat. Thedas is a big world, and the idea that the Warden/Hawke should be important to the storyline is really more the result of OUR bias towards the character than any sense of "realism". Because they really don't have to be, there's so many ways the writers could explain why they're not at the forefront of the conflict.
The Warden and Hawke became heroes because they were at the wrong place at the wrong time (well, the right place, really), and that's why they don't HAVE to be prominent in this conflict. They could jsut be _elsewhere_ when things get going, and so never get the opportunity to take the lead against this threat (and in the Warden's case at least, this is assuming he/she would even care/is still alive). This is the very same reason the Inquisitor becomes the Inquisitor: wrong place, wrong time, he/she gets the fade thingie and ends up having a new destiny (or some such).
Thedas is a big place, and there's plenty of room for new heroes for every game, and for previous protagonists to be off doing Other Things. These could be Very Important in their own right, of course, but we just don't need to know that because the current game is not about the old protagonists. And they certainly don't need to be.