That said, I think the fears about many people refusing the vaccine are completely overblown. All of the folks who I've talked to who are concerned about the vaccine have expressed willingness to get it after it has been out for a few months without major side effects. They wont qualify to be first in line anyways, so they'll have to wait regardless.
So it's entirely reasonable to just study symptomatic cases in these trials.
The more of the population unvaccinated, the larger population available for new strains to generate in, the higher probability of multiple strains.
It's not guaranteed the current vaccines inoculate against new strains, so you could be right back at square one next winter, with a new virulent strain.