Public health figures in CA are saying that it could be two years before everyone in the state who wants it and qualifies can be fully vaccinated; they don't think that even the seniors will be finished before June. Considering that healthy young athletes are going to be in the lowest tier of those who are eligible for the vaccine in this country, it is unlikely that the American Olympians could be vaccinated in time for Tokyo. Japan is an island nation which has had relatively few cases, like Australia, and you have seen how rigidly the Aussies have controlled entrance for the Open, so it seems unlikely that the Japanese will relax their requirements.
Of course, the US could make a special exception for their Olympians, but there would be a lot of bad feelings from those ahead of them in the line. The athletes from poorer countries which are having problems getting any doses of the vaccines at all would be disproportionately affected at the Olympics this summer.