Why? They are literally the best equipped species in the lore for an undertaking such as this, as they have been nomadic wanderers looking for planets to settle for 300 years. Leaving out their input would be utterly contrived, with the only justification being not wanting to deal with certain ME3 story permuations ( some of which the writers have already ignored to shoehorn in the krogan anyway), or subjective dislike.
What focus did they have? They weren't even in the first game apart from a single member of the species serving as an exposition device for their lore in a few of her conversations, and they shared a side arc with the geth in the next two (of which the krogan and every Council species also got one of, more or less)? We've had 1 quarian companion compared to 4 asari, 2 (now 3) krogan, and 2 turians, for example. Hardly a huge focus.
It is precisely because of their usefulness that they could be left behind, narratively. Too useful.
That said, I think they'll be in the game and play a good role. At least I want them to.
They were one of the most focused on species in the trilogy. In terms of content focus throughout the trilogy, as a 'species story', it was pretty much (in no order): Asari, Quarians, Geth, Krogan. The Genophage arc has Turians and Salarians as secondary to the Krogan, and the trilogy increasingly shifts majority focus on the Geth, to being more about the Quarians (or at least equal) at the point of ME3.
Basically I'm saying that they got a lot of story for such a low population. Most of it may have been in ME3, but it indeed was tied into the Geth story which was a big part of ME1 (even as one could ignore what the geth were and just pew pew them), and at least a few missions of ME2 (even if pretty much all optional).
I'm not saying they had the MOST story. I'm saying that I wouldn't be surprised if the next game has the Quarians have less ratio of plot than ME3 did. And I say the same about Geth and Krogan. I WANT, and do THINK that ALL THREE to have a continued species storyline, but I really do doubt (which I'm pretty sure you'll disagree with) that Quarians will be a big part of a lot of MEA. Present throughout? I hope so. Important at some point in the main plot? I'd love that. Important to a bunch of bigger optional missions? I'd love that as well. I just don't expect an 'arc' that is pretty much devoted to their problems. Their problem was Rannoch. Now they can help with other problems, and we can learn more about them in the process.
It was just that if I had to pick any species to not be part of MEA, it'd be Quarians even if just for them getting a good chunk of ME3's plot already, whereas it seems Bioware wanted (from their convention statements) to explore more to do with Elcor, Hanar, Volus - which very well could happen because things seem to be all about a bunch of various peoples working together for a new home instead of contributing fleets and war assets.
EDIT: By huge focus I just mean I don't expect a Rannoch arc (which I admit was tied in with Geth) ever again. No sequence of a few mandatory missions that always have to do with Quarians and narratively means a big thing (getting Quarian/Geth/Both fleets). That's it. Again, personally, I want Quarians and I want them to play a big role; I'm just not so supportive if they end up being very important and a big part of like 2+ mandatory core plot story missions in a row. Not in this specific game.