There's a "nothing in real life is ever this simple" formula about what fraction of the population needs to be immune ("have a robust immune response"), before you can stop worrying about the spread of a disease:
If R₀ is 10, which is not implausible for some of the observed COVID-19 variants, you need 90% of the population to have a robust immune response to keep the disease from spreading using herd immunity alone.
Knowledgeable people who are not doing the "nothing is ever this simple" version are saying things like "at least 85%" about the necessary vaccination level for herd immunity; the current vaccination rates, even in the US, aren't anywhere close to enough to keep the disease from spreading.
If 85% vaccination is required to get to herd immunity, we can't get there this year; at least twenty percent of the population is too young to be given any current COVID vaccine, even if absolutely every adult gets vaccinated with an mRNA vaccine. Approvals for use as paediatric vaccines are being sought for all the COVID vaccines, but right now the age cutoff is 18. Several of the vaccines can't get to 85% effectiveness, either; so far only the mRNA vaccines have effectiveness levels high enough that, in principle, vaccinating absolutely everybody would be sufficient to extirpate the disease.
We know, from several national examples of effective public health, that you don't need a vaccine to extirpate the disease; you can institute movement controls, food delivery, necessary "hold in place" payments so people can not work and not starve, enforced quarantines, and a robust track-and-trace system, and extirpate the disease that way. It'd be really expensive to do that now, rather than in the beginning, but it could be done. Effective public health measures are not being done as a matter of deliberate and conscious profits-before-people policy, targeting reopening rather than extirpating the disease.
The variants now spreading affect children and young people more seriously than the wild type.
We can expect, if we treat some level of vaccination -- any level of vaccination we can achieve this year -- as grounds to generally drop COVID restrictions, that we will see the continued spread of the disease. It will produce many more dead children compared to the wild type, and it will (given the Brazilian example) put vaccinated people into hospital, possibly in large enough numbers to overload the system. (The system overload threshold is decreasing over time, as health care personnel are being expended by the strain.)
What the vaccines accomplish, even the "this won't stop spread" vaccines, is to greatly reduce your odds of harm if you should contract the disease. You are much, much less likely to die or to require hospitalization. This is useful and worthwhile; by all means get vaccinated. Just remember that this is a personal-scale benefit, not a systemic solution.
The other thing the vaccines do, because they are not sterilizing vaccines, is increase the odds of worse variants developing in a given individual; more infectious variants arise when the virus spends a long time reproducing inside one host. That is, the virus and the host's immune system stalemate, and the virus reproduces many more times than usual, increasing the odds of a mutation that increases virulence happening. This is a big part of why you don't want people catching the disease in the first place and why the "just let it burn through the population and it's over" take is extremely dangerous. The sixty percent vaccination rate that's guessed as the eventual full voluntary uptake is, as the sole public health measure, a recipe for worse COVID.
The policy that comes out of this ought to be:
- vaccinate everybody as soon as possible, starting with the people in the groups most likely to catch the disease
- adopt the full public health measures, including movement controls, enforced quarantine, and a required complete economic shutdown so people can stay home
- an explicit requirement that reopening happens if and only if the disease is extirpated; no level is acceptable