Note that the locations you mention that have higher infection rates for vaccinated vs. unvaccinated are also locations that have very high uptake rates. As such, this is expected as a matter of mathematics. There's an excellent article on it here:
As to the unvaccinated being the source of variants, let's look at where the major variants have come from, shall we:
Kent, UK, just prior to the start of the vaccination programme, in an area of the country through which many international travellers pass (multiple airports plus the channel tunnel and ferry).
South Africa, in political turmoil and as at June 2, only 2% of the population had been vaccinated.
Brazil, Bolsonaro is the South American Trump, 'nuff said.
India (aka Delta variant), huge population, low vaccine uptake (and suggestions that their death rate is four times what's reported).
The bigger issue is social policy around the herd imunity tipping point (which the US will never reach).