I would try to remove the plywood, which might be nailed as well as glued. Try on a straight step first. i agree with you that a runner on those gorgeous oak steps would look best and make a great impression. So I think it is worth the effort.

Get a price to refinish / replace staircase and a price to replace carpet. You will not recoup your money on either choice imo, so then you can decide what you want to do.

We have gotten estimates for refinishing and carpet - assuming that the existing treads are salvageable, refinishing wasn't that much costlier overall (depending on the price per sq ft of the chosen carpet, of course). However, that didn't take into account the glued-on plywood or the likelihood that the original treads are toast. Refinisher charges $250 per tread to replace, which blows the budget entirely.

I have also seen some photos of staircases with just one full wood tread on the bottom step, with the remainder carpeted. It's a bit odd, but if done right it kind of emulates the look of a runner. I was also thinking that I could remove the plywood just from the rounded end of the bottom stair and refinish the wood, so that bit isn't wrapped in carpet, and then run the carpet straight down from the preceding stair. The carpet would sit up higher than the stair, but I could cover the bare plywood edge with some molding or something.

Also, if the treads are a mess after plywood removal, I assume painting would require less work than staining?

There has to be a reason the plywood has been added. No one would add plywood, just for fun. someone took a lot of time, and patience to get that curve just right, so there had to be a darn good reason for that. Chances are that the stairs themselves are not in great condition and unusable. I would pick a nice carpet with a pattern, that doesnt show dirt so much, and recarpet them. New owners might even appreciate the carpet, if they have small kids or pets. To be honest, carpet is safer than bare steps anyway, especially, for children and older people.

I’m with @cat_ky. Surely there’s a good reason for the plywood? It’s a bummer though. But if you end up carpeting, I would do a fun texture or pattern on the stairs. And the stair carpet does not have to match the upstairs carpet as long as the two go together.

You may be right about the plywood. I was guessing they did it to even out the rise between steps (the bottom step has a double layer while the others only have a single), but it could be that the treads are completely unsalvageable. The previous owners mentioned that they preferred carpet on stairs for safety, but they fudged the truth about a LOT of the repairs/work they did.

Yes, if we end up doing carpet we plan to do a short-pile pattern on the stairs that complements the hallway and bedrooms. There are a ton of doorways in the hall, so to avoid a million transitions we will probably do the BRs and hall in the same material - maybe a cut and loop. Right now we have the same carpet everywhere INCLUDING the stairs, which IMO just looks cheap (not to mention that it's high pile and totally inappropriate for stairs/high traffic areas).

I tried. lol

I like the look of herringbone.

Plywood is there because there is lead paint on it. If, you want wood treads, you need a remediation company to do it. Recarpet is the most economical.