Well, getting arrow spine right is pretty much the single most important part of tuning your bow. So I reckon I'm taking it for granted that one has the proper arrow spine to start with. It should be a non-issue when talking about the difference in relative accuracy of a rest vs the shelf.

And, naturally, we're mostly talking recurves here because putting an elevated rest on a longbow is kinda.... creepy.[:'(] That's what makes an amazing shot with a longbow even more amazing.

It only takes a small observation and a tiny bit of contemplation to ferret out the reasoning in this matter. If shooting off the shelf is as accurate as shooting off an elevated rest, then you'd see many Olympic archers shooting off the shelf. They don't. NONE of them.

I mostly shoot my hunting bows off the shelf - or off my knuckle with my selfbows. I like the advantages it has for hunting and because, as you say, one can shoot extremely well that way. If I was out to bust pop a 300 on an indoor round though, I guarantee ya I'd be using an elevated rest. The improvement is a matter of degree. If you can shoot a 3" group at 20 yards from the shelf, you might do a 2" group with a flipper.

Just speaking for myself, I agree with the old timers. Back when I was competing seriously, my field archery target scores were a good bit higher and a lot more consistent when using a rest than they were when I shot off the shelf.