It would be nice if they're extreme talking points, but these are routinely presented by the media and public health agencies. For example up until very recently claim (4) was being made in Germany, and claim (3) is basically the claim underlying any implementation of vaccine passports - of course, we may suspect they are in reality merely means of extra-judicial punishment, but governments officially deny it.
Regardless, whilst these claims are "extreme" in the sense of being phrased in absolutes, they aren't "extreme" in the sense of being rarely believed, are they? Not only do they crop up all over this thread but in the very article the thread is about, Angelas Merkel, not exactly famous for being the Queen of Extreme, says "The fourth wave must be broken and this has not yet been achieved" which is simply another way of saying (3) and strongly alluding to (1) and (2).
Also:
"it drastically reduces the likelihood of infection, which drastically reduces the transmission rate, and recent studies have shown that it does also reduce the likelihood of transmission directly"
Let's break this down:
1. Infection rates. Health agencies claim it reduces the likelihood of infection, and at first it genuinely seems to, but the only one that is willing to show the actual raw data before they wildly alter it using statistical techniques, is the UK HSA. Their data shows that by now the rate amongst vaccinated people is actually a lot higher than among the unvaccinated for some large age groups! This sounds like it should be impossible, but it turns out to have been observed in pre-COVID times with other vaccines.
They have been reduced to claiming that comparing case rates between vaccinated and unvaccinated people isn't a valid way to determine if the vaccine works, due to vague behavioural differences that they speculate must exist but have no proof for.
2. Rate of transmission. Not for the first time, we find that epidemiological studies aren't worth much. Can you cite yours, so we can see when it was written? Because once again UK data contradicts it (or it does now at least):
https://www.thelancet.com/journals/lanepe/article/PIIS2666-7...
"In the UK it was described that secondary attack rates among household contacts exposed to fully vaccinated index cases was similar to household contacts exposed to unvaccinated index cases (25% for vaccinated vs 23% for unvaccinated)."
No real difference in transmission at all. Actually slightly higher for vaccinated people but let's assume that's not really significant.