I find that I like the look of short seat stays, as if hellenic stays were attached and ended at the seatpost. I realize that most of these are aluminum or carbon fiber, but are there problems with building such a frame from steel?

it's generally a good idea to reinforce the area where the seat stays intersect with the set tube with a sleeve. Same with the top tube. If the top tube and seat stays don't intersect close to each other, you need two reinforcement sleeves.

Most steel frame bikes have steel seat stays as well, so I don't see why not you wouldn't be able to build a seat stay with steel.

How short you are planning to make it might be the question here.

I am aware of the need to sleeve the seat tube or use a thick wall non-butted seat tube.

I haven't actually laid out the geometry but I can't see the seat stays being longer than 20 inches. Can I assume that this would give a stiff ride if the seat stays aren't sufficiently tapered?

I don't think I would worry about that if the structural concerns are taken care of

So the longer stays are just because it's easier and less work?

it's a better structure to have the seat stays meet the top tube. Many bikes have broken at the seat tube/seat stay/top tube junction. It's probably just as common as breaking at the bb and more common than breaking at the head tube.