Also your claim about people with the vaccine still being infected/infectious is a pretty bold claim. That's not settled science, and it's quite likely (and consistent with other viruses and vaccines) that the immune system fights off a COVID infection before it becomes communicable in most immunized people. There are definitely breakthrough cases but it's not clear that the majority of cases behave this way.
Of course we'll likely never know for sure because of the stubborn 30-50% who refuse to get vaccinated.
I don't understand this. My conjecture is that people who are infected but asymptomatic due to vaccination would have no reason to show up in the case counts either way, since they would not seek out being tested at all.
As for being a bold claim, it's established science that vaccination can not prevent infection. The virus can still enter your system. I agree that it is a debatable question as to how many and to what extent those vaccinated people are infectious to others.
What is the evidence for this? Vaccinated people are capable of spreading the disease just as easily as those who aren't. And since they're much more likely to be asymptomatic, may be more likely to spread the disease unknowingly.
Those without the vaccination are more likely to end up in hospital, but that says nothing about how the disease is actually being transmitted.