https://www.nature.com/articles/d41586-021-02689-y
https://www.businessinsider.com/delta-variant-made-herd-immu...
But, have you heard of herd immunity?
I have heard of herd immunity. Unfortunately because the vaccines aren't really sterilizing and the Delta variant is so contagious there will be no significant herd immunity effect to protect those who lack immunity. Over the long run we'll all be exposed to the virus multiple times no matter what we do. That's why I recommend that everyone eligible get vaccinated to protect themselves against severe symptoms.
Is your latter conclusion re herd immunity being impossible supported by the literature, or at least a mathematical model? If R0 goes below zero the community is protected. The vaccinated fraction might have to be large in order for this to happen, but that's also the case for the measles. You're stating that it doesn't matter what this fraction is, even if one person isn't vaccinated they're eventually going to get infected.
There is no reasonable hypothesis for how humeral vaccines could induce antibodies in the mucosae, therefore stop viral replication there, and therefore reduce shedding and hence infection of others. Nasal vaccines perhaps, which are an exciting development and may be what actually ends the outbreak, but not the current lot.
To be able to claim the current vaccines reduce spread you either have to propose how humeral vaccines delivered to the blood could induce T cells in the mucous membranes of the nose and throat, or suggest another mechanism by which the virus can spread.