I believe the anvil is necessary because the priming compound needs to be pinched between two hard pieces of metal.
An unwarranted assumption. Some fiddle-de-de might be necessary (nitrogen iodide as a component?), but I'll bet a pellet of regular old priming composition would go off by being smacked between two pieces of plastic... presumably combustible. And I think a molded propellant with the primer pellet stuck in the base and covered over with a thin layer of combustible coating would go off.
Don't forget that in current practice, a lot of the approximately 12 in-oz of firing pin energy (minimum for .22LR, IIRC) has to go into deforming the primer cup --or rim.
If such a molded/integral primer "cartridge" were built, I'll bet it wouldn't be too hard to arrange matters so they could be used in a conventional firearm with few modifications except maybe for sealing the firing pin hole in the breech face.... maybe with a rollsock arrangement.
If you're feeling clever, put piezoelectric primers in conventional brass cases with the wire leads sticking into the powder area. To reload, just put in new powder and a bullet; there's no need to put in a new primer. Since the primer can be made integral to the case, and of arbitrary thickness, you might be able to run at higher pressures too.
Kind of obviates the purpose-- to reduce brass consumption. Actually, I wonder if such a method might ultimatately be "shrinkified" to fit in a regular primer pocket. Somebody (I forget who, but someone will jump in with correct data) now has a battery-operated system for firing BP guns. I wonder if it can double as a Tazer...heh.
And actually, the biggest problem I see with respect to caseless ammo is clearing after a misfire or decision to unload the arm, not the technology of manufacture or adaptability to conventional firearms.
(Aside): Many moons ago Herter's had an all-plastic shotgun shell --all pretty transparent blue polycarbonate, but you still had to use a standard 209 in the rear, and you couldn't crimp them, you had to use top wads with a slight roll crimp.. I reloaded them a couple of times, then kind of let it go, since I had plenty of AAs around anyhow. However, the pressure levels in shotguns is much less (what, around 25,000 "psi"?) than in a modern rifle... but it's close to pistol pressures, so maybe full plastic cartridges are a possibility for handguns. I think the .45ACP standard pressure is around 15,000 "psi," if I recall correctly. And Speer used to make plastic cases for firing plastic practice bullets at low (primer only) pressures.
Here's a gun what don't use no cartridge case:
