so my question is would carpet installers prefer to wrap the treads before they’re installed, or am I making it more complicated than it needs to be?

You should ask the carpet installers.

It does not matter if anyone else ever did it before. When you select a carpet installer, ask them.

I don't understand how it would be possible to wrap carpet on treads before the treads were installed. It seems that would be possible only it there were no risers. If you're talking about individual carpet pieces with a preformed nosing, I see no advantage to installing them before the treads are in place.

Yes...and if you are proposing to fully wrap the treads on all sides and edges and therafter installing...before the risers are installed...how will the risers be installed tight to the treads?

I think the answer may be "yes", carpet installers would like to find the simplest and quickest way to install the carpet. The stair fabricators, on the other hand, may have serious reservations about finishing the job.

Have you considered you may need another concept?

Well, you certainly can't put carpet between the finish treads and the rough framing of the stair or between the finish treads and the risers!

I think the OP might be thinking of "bullnose carpet treads" that simply slip over the wood treads. Its generally a DIY product but a carpet store might offer more choices and safer installation.

I'm not understanding why you want to do this?

I don't know what you mean by "wrap the treads". If the photo above of bullnose carpet treads doesn't show what you want, I don't know of another interpretation that is feasible or legal. The carpet can't be trapped under the tread; the tread would not be stable and could cause a fall.

"Wrapping" the treads (whatever that means) before installing them as part of the stairs is probably exactly the wrong sequence of construction, as far as tradesmen are concerned. First the stair fabricators finish the stair. Then the carpet boys come in to "wrap" the top of each tread, after the stairs are completed and the fabricators have left the site for good.

Are you doing all the construction yourself, and not using tradespeople?

If so, you may certainly follow any sequence of construction you wish.

I'm curious, however...what's the difference in the photo you posted directly above, and the photo above that posted by RES? They look exactly the same to me...

In order to carpet the entire width of the tread including the nosing, I suspect the top of the riser would need to be stopped a quarter inch below the tread, then a carpet installer would be able to tuck the carpet edge into the notch. That means the tread nosing would overhang the rough stair framing about 1 3/4" putting additional stress on the tread but it will probably be OK. I don't see any advantage in carpeting before installing the treads, in fact, I doubt a carpet installer would do it.

Ignore this idea if it's crazy....

I've seen treads with piano hinges (I think that's what the hinges are called lol), where you can lift up the treads. Usually, storage space is built into the staircase, and the storage is accessed via the tread. Excellent space to store gift wrap, umbrellas, or the blueprints/sketches of the house. :-D

Could a tread like that be successfully "wrapped"? The carpet may have to stop on the outermost sides, before coming into contact with the hinge, but does anyone know if that might work?

Whatever is done, the tread must be rigidly supported so it does not move when stepped on.

Have you considered how to finish the exposed lath wall adjacent to the stairs, now that the stair framing is in place? It's another sequencing issue...

If you intend to wrap the carpet over the end of the treads I would advise you to reconsider and use a partial covering or a runner.