Saying "6 out of 8" of the inquisitor's LIs won't be present in DA4 is just speculation.
Most of our former LIs won't be companions: we know that. But there's nothing to prevent all of our former LIs from returning in one way or another, via unique encounters specific to whatever relationship we happen to be in.
Inquisitors who didn't romance anyone in DA:I would, of course, have their choice of a hottie from the new line-up, and inquisitors in relationships would have to decide whether to betray their existing lovers or remain faithful.
See -- it's not that complicated a problem to solve. In fact, having to resist temptation is an interesting personal conflict that can spice up an RPG.
As ever, everything depends on the quality of the writing and presentation.
P.S. And betrayal isn't the only way to end a relationship. Maybe you and your existing LI can have a fairly amicable break-up if you meet the new love of your life in DA4.
Fiction is drama, no? Drama is the reason we play BioWare games. By saying, "Get rid of the inquisitor so that our romances are smooth sailing in the next game!" you're saying, "I want less drama!" -- and that's absurd, isn't it? You wouldn't watch a thriller at the cinema and walk out because it's too tense and too interesting. lol
Okay, but being realistic about how Bioware is going to approach the idea of their audience, they are not going to go this route and pi$$ off a vocal percentage of their fans. Take a look through the character threads to see how passionately people discuss their romances and favorite characters. If we have Inky as PC again, following this idea, Bio would have to:
write dialogue and make cameos for DAI LI's who are in the game but not returning as companions
write dialogue and a romance path for new companions who are romance-eligible
write dialogue for an Inquisitor who did not romance anyone in DAI but is now romancing someone in DA4
write dialogue for an Inquisitor who did romance someone but is now pursuing someone new
write dialogue for breaking up with former LI or cheating with a new LI
hire voice actors to record all of these dialogue permutation, including hiring the returning LI dialogue, which is extra if they otherwise would not have shown up in DA4
and most importantly...deal with the fallout from fans for being able to break up with the love of their life from the previous game just for a fling! or be mad that in order to experience a new romance option, the fans' PC must break up with their current partner.
This really isn't feasible from a fiscal perspective or from a consumer-relationship perspective. And this is for the small percentage of players who finished DAI and played Trespasser. Which I assume is not the majority of the players Bioware hopes will purchase DA4
Come to think of it, if they made the inquisitor v Solas thing an awakening style expansion that would be awesome. Those of us that want to play the inquisitor and take down Solas personally would be able to, and those that don't would be able to start fresh in the next game.
This is probably the only method in which to appease those wishing a personal resolution between Quizzy and Solas, and those wanting a completely new DA4 PC. Unfortunately, the chances of this are...infinitesimal.