You see this in upscale hotels all the time. granite, marble etc slabs for shower surrounds. also for flooring actually.
With stone getting cheaper, i think it should be not be that much more expensive than tile but somehow it is hard to find tradesmen who know how to do this in america.

Irrespective of the staining, etching, and scratching potential issues with marble. It's very heavy, and will need a powder coated steel ledge attached to the studs to support it if you are using an acrylic tub. A cast iron tub might be able to take the weight. Consult with the tub manufacturer. At an average of $100 a square foot, it's also not going to be inexpensive. I'd expect 4-6K for the average tub alcove, depending on quality of choice and how tall you take the slab.

I've seen numerous pictures of [marble slab showers on Houzz.com[(https://www.houzz.com/photos/marble-slab-shower-phbr0lbl-bl~l_45924). Sorry I don't have any advice on upkeep, but I must say they are absolutely gorgeous!

Shower panels are thinner than countertop material. Usually 1/2".
Some are thinner (installed on aluminum honeycomb for strength). It may even end up lighter than tile.

Here is a link that might be useful: shower stone panels

You might want to check out ForzaStone. The panels are real stone but very thin with a backing. They are much lighter than typical marble slabs. They come in large sheets so few grout lines.

www.forzastone.com