Yes, if I was to choose (for a studio desk) then padded leather on a piece of wood would be the best option.
You basically need two pieces of wood, one that holds the arm rest and the other attached below it (where the staples are, like a sandwich) unless you find a better solution.
I did a mixing booth with carpeting and getting the staples covered is indeed a tricky part. With thick carpet it isn't much of a problem as long as you get them punched in deep enough.
Then I started working on a console frame (like 12-16ch) and the padding was styrofoam covered with leather I cut from a pair of pants (it had a seam or two iirc, and I never got around to attaching it "properly", or adding the extra piece of wood as for that matter)
The thing with "real" leather is you can keep it clean and shiny with detergents but it smells kind of weird (think of a new car scent).. fake/synthetic leather is much cheaper though and doesn't necessarily come with seams but is prone to ripping (ie. it's like rubber, Latex etc), the thin, small pattern one I wouldn't recommend either because of the obvious wear and tear (the stuff they use to make wallets etc) but the heavier/thicker it is is the more it's likely to cost so keep that in mind when assessing prices (I was once asking for fake leather yard prices, ~120cm wide 3mm medium thick cost like 30eur and upwards per meter, there were a couple of colour choices though like bright red etc which is the main advantage of it I think)
The problem with padding is you can't properly glue it in place along with the carpeting (and you're well on your way to build a sofa)
If it's a touring/live console then I'd either leave the arm rest out or use a synthetic material like Tolex (and you don't really need one in desks smaller than 19")
You could also consult companies that make computer mouse mats if they have some sort of modern solution but unfortunately custom stuff usually comes with a price (the results could be amazing though)