It won't happen, because the explicit arguments are just pretexts. After The Lancet/Wakefield and Jenny McCarthy (and other popular media figures), the word "vaccine" is now simply triggering of aggressive suspicion. That media panic combining with:
1) the 80s New Age/Self-Help/Healthy Living/Naturopathic flakes,
2) the suspicions of black people who are generally neglected and sometimes abused by the health care industry (over a very long term with sign-off from regulators),
3) and the religious fundamentalist divine punishment crowd (disease exists to punish weakness and evil), and
4) the factual observation that the healthcare industry in the US is hopelessly corrupt from top to bottom, and will not change no matter how strong the political will of the general population, or how organized it is,
...and all combinations thereof, means that this is going to be something that we have to deal with forever. It has nothing to do with whether the vaccine is new or experimental, it's that it's a vaccine. We still don't have universal vaccination for HPV, and that prevents cancer.
The media blames vaccine hesitancy on Republican hucksters, but that's just because they're centrist neolibs and that's what they're paid to do. Republican grifters take advantage of whatever's available; this week they actually became animal rights activists in order to attack Fauci:)
The anti-vax feeling is deeper than that; it's become hopelessly tangled into religion, identity, and anti-authoritarianism. It's not going away. Covid-19 was actually pretty mild when it comes down to it, when a real disease comes along, we're all dead.
I'm actually on a personal countdown until I hear the first argument that this safe, effective, experimental pill is a reason not to take the dangerous, pointless, experimental vaccine, and that big pharma wants you to take the vaccine instead of the pill because reasons.