Going to brake down the question into a couple of parts, I apologise if everyone already knows this crap.
Soft vs. Hard : you can get some really really hard lead bullets. The stuff buffalo bore sells for dangerous game hunting is crazy stuff. Cast lead bullets that hang together punching though a buffalo shoulder at 2000 f.p.s.+. Plated bullets like Rainier ballistics stuff is really soft. So soft that you can easily deform them with a strongish taper crimp. They don't tend to deform during shipping though, so I don't think that' a concern. Even the big-boy .50cal bullets I use in my DE don't seem to dent just rattling around in their box.
Lead bullets and fouling: This might have something to do with the move away from lead. Unless you're shooting a polygonal rifled barrel, it will foul, but only to a point, then the lead reaches a stable level with each round not depositing, or perhaps cleaning as much as it's leaving, lead on its way out. The problem with polygonal barrels, as I understand it, is they don't exhibit this self-cleaning mechanism. You're probably fine for some number of rounds between cleaning, but after that the bore can get tight enough to cause a failure. I think this is the "some glocks can shoot lead, some can't" thing you hear. Some people clean up after 50 rounds, some want to shoot 1k between cleanings.
Bullet shape: I know wadcutters and semi-wadcutters were popular with accuracy-heavy competitions, I heard they punch cleaner holes in paper? Perhaps that's part of the falling out of favour?
Why Jacketed: I think this is driven almost largely by indoor ranges requirements, which is questionable at best. I never went to a indoor ranges until I moved up here, so I don't know when that started or if it's always been the case. This is kinda dumb because a) almost all the pb vapor is from the primer b) unless you're shooting total metal jacket bullets, you've likely still got exposed lead at the base of the bullet against the powder where all this lead is supposedly being vaporized. What does get vaporized is the bullet lube, and this can cause excessive smoke. Unique in a low-pressure .38 load under a cast lead bullet is a serious smoke-show. This can be a problem for modern pistol games for obvious reasons.
Shooting plates : just to clarify, I don't think that the potential for ricochet of the bullet is likely to happen if you're shooting at properly designed plates at acceptable velocities (~750fps is required for steel challenge). The problem is the jacket coming off the lead and causing dangerous splatter on improperly set-up steel. Talked to a guy that needed stitches in his face due to such an occurrence one time.
I see folks that still used cast lead bullets, but with moly/plated stuff being almost as cheap, and acceptable at more indoor ranges, I think that's why the re-loaders have gotten away from them.
One other cool deal with moly bullets for competition : they will crono faster with the same powder charge as jacketed/cast bullets. More power factor for the same recoil.
Man I kinda rambled there....
