Is there at least one 22lr pistol that will shoot the cheapest 22lr ammo really well?
I'm sure there is, but I'm also sure no one can definitively tell you what that is. Because no one knows, for certain.
We can tell you what our guns do, and don't but you could have exactly the opposite experience with an identical gun.
As a class, .22 semi autos are about the most finicky firearms out there, when it comes to what they will run well on, and what they won't. Some eat everything, some one run well on certain things.
And, you cannot count on the pistol's price and quality as any guarantee that it will run "the cheapest" or any brand specifically. Every gun seems to be an individual in this.
A friend's S&W model 41 had numerous misfires with a batch of CCI Blazer we were shooting. My old Ruger Mk I ate that ammo flawlessly. A different batch of ammo might have given different results.
And, other things than just the ammo matter, as well. My old (83) Ruger Mk I has been about 100% reliable with everything I've fed it, with ONE magazine, and only about 80% with a different magazine.
We can give you opinions to answer your question, no one can give you any fact, other that what the pistols we have, do.