No, I think Fauci is within reason.
Let's take the UK, which we must suspect has had a similar number infected to the USA, and has a similar number of people vaccinated (total vaccinations very similar, although the UK has more people with one shot out of two, and fewer with both). So infections in the UK should be going down, right? Er, no. Infections have actually gone up about 25% since relaxation of social controls in early May. That's pretty interesting, given over 50% of the population should be largely immune due to vaccination, plus all those naturally infected.
Also, there's a great deal of misunderstanding and general dickheadery going on. Let's imagine that "herd immunity" were reached at 50% of the population having been infected. So, the infection rate should decrease overall. Okay, fine. But when that herd immunity kicks in, the R rate is (theoretically) going to be ~0.99: actually, a very substantial number of people can still get infected, and the rate of decline of the disease is very slow. Also, we're talking about national; what this conceals is that there are likely to be localised areas where there isn't herd immunity where the infection can still propagate strongly.
Of course, if one understands R rate, this is in practice measured by infection rates. So of course you can have a national R rate under 1, until the disease hits a localised pocket with low rates of immunity, at which point infections rise rapidly that could send the R rate over 1. So this is why it gets complicated: national vaccination rates do not actually tell us whether certain subgroups of the population are safe.
So when we think about the task of the guy who is trying to ensure the continued survival, health and wellbeing of US citizens, his job is to encourage vaccination and take a caution-first approach to the data likely to save lives. Naturally, all the forces of Fauci-haters will disagree: the resentful Trumpistas who can't forgive him for disagreeing with their cult leader, the anti-vaxxers, the capitalists who want everything opened so they can earn more money, and the "But mah freedom!!!" brigade who think other people dying is a worthwhile sacrifice so they can eat inside at a restaurant and not have the inconvenience of wearing a mask (because a facemask is SO much of a burden). Obviously, these people will reach around for anything and everything to diss Fauci, because they have other objectives than the survival, health and wellbeing of Americans. Some of them get to write columns for national newspapers to spread their disagreement. And all the other ones will nod sagely at this article telling them what they want to believe, praising it to high heaven for being "correct" and Fauci "wrong", because mostly they don't have the faintest fucking idea, but they want to believe what they want to believe.