As a famous individual once said, the more you test, the more infections you are going to find.
Just about the only thing that person said about COVID that was actually correct...
Everything you said is correct. The key difference with COVID is how we test for it, as it's one of the first viral diseases that has been using the ultra sensitive PCR technology as a diagnostic test for everyone, not just symptomatic patients. I could go on and on regarding this, but will leave this alone because it's the virological equivalent of "if a tree falls in a forest and no one is there..."
And yes, NO VACCINE is 100% effective. Never has been one, and I doubt there ever will be one. Yes, many moan and piss that the COVID vaccine and all boosters is not 100% protective, but these are the same people who forget to mention that even the "natural immunity" they tout also isn't 100% effective; folks who have had the disease are getting reinfected too. Without going on chapter and verse, just remember there's another coronavirus that people get reinfected by all the time, it's a few strains of the common cold!! And there is no vaccine, nor lasting immunity derived from an infection...
In the case of "breakthrough infections" of vaccinated folks, the downside of using a PCR test as a diagnostic test becomes quite apparent. As you said, a vaccine is not like asking Scotty to raise the shields. For a vaccine to work, you have to get infected, because that infection alerts your vaccine-primed immune system to get down to business. So asymptomatic or not, COVID or any other disease, for your vaccine to "work", strictly speaking, you have a "breakthrough infection" because you'll have a positive PCR test. It's a matter of immunology and assay design...
OK, enough from me. I'm sure all the arm chair, self-anointed Virology PhDs that lurk here, who got their degrees from matchbook covers will now chime in with their edumacated treatises regarding COVID. At least in this thread, I nuke them at will with no guilt whatsoever...