If you look, a 22 Long CB is quite a bit shorter than a 22 LR. I think that is because the CB bullet is actually a short bullet, not a LR bullet. I tried a 22 Long CB out of my CZ 452 and I had a shotgun pattern group at 25 yards. I think this is because my chamber is pretty tight.
I'd like to try a rifle that is made to shoot shorts, longs, and LR. That would be a lot of fun to pick up one of those Henry lever action 22's because I have a Winchester 94 30-30. I'm sure those Marlin bolt tube rifles that will shoot shorts are pretty accurate too.
This goes back to the OPs question. Most all tube feed rifles, single shots, and revolvers are DESIGNED to shoot shorts, longs, and long rifles - even if they are just marked 'long rifle.' There is just no way, though, to make any .22 rifle accurate with all three types of ammo unless it is a 'switch' barrel rifle. I guess this would be easiest with something like the Thompson-Center Contender. Their custom shop does offer a barrel listed as for '.22 short match.'
The problem with accuracy is due to the twist rate of the rifling, not so much the chambering. Most .22s are built with a 1-16" twist, made to best stabilize long rifle bullets (33 to 40 grains). Shorter (hence lighter) bullets like in shorts and CBs do not do well with this twist. They prefer a twist rate of 1-20" to 1-24" to shoot accurately. Most shorts and CBs shoot a 29 grain bullet. I think Aguillas are 20.
Over the years, many rifles and pistols have been chambered specifically for the .22 short. I think some international handgun competition is done with .22 short chambered guns. Right now, some custom Ruger 10/22s are short chambered and rifled. I have seen the parts available to convert them yourself and they function just fine with the new components. The trouble with have a gun specifically chambered for the .22 short is that not only is the twist too slow for long rifles, but the chamber is too short for them to fit. I suppose one could chamber a gun with a long chamber and a twist rate for .22 shorts, but then it would not be accurate with long rifle shells.
So, in end, we have many rifles rifled and chambered with long rifle specs than can shoot shorts and CBs. They work well, just not as accurately as some of us would want. They do fine, though, on close cans, rabbits and squirrels as long as you keep appropriate expectations. I shoot CBs and Aguillas out of a several of my .22s and find it fun.