Israel study demonstrated just that recently
The mRNA vaxes target only the spike protein of the virus. And maybe only a portion of that spike. All the vaccines do. To do more requires more time, and the goal of Warp Speed was to get something out within a year.
The J&J vaccine is a vector vaccine. It’s not mRNA but like the mRNA vax it teaches your own cells to make the spike so that your immune system can learn it.
The Novavax vaccine is a subunit protein vax. It has its own spike for teaching your immune system. It isn’t telling your own cells to make the spike.
Anyway the vaccines all work, but only against variants having the original spike. Delta has a mutation that changes the spike enough to evade the vaccines. So delta is getting passed around while the original virus stalls out.
If you catch covid your immune system learns the whole virus and not just the spike. Wild-type antibodies. So it should be able to defeat the virus no matter what the spike looks like.
A whole virus vaccine would be similar to that, creating Wild-type antibodies. But ADE was a problem in previous attempts to create whole virus vaccines for SARS-1 and MERS. And ADE can kill you. It may be awhile before there’s a whole virus vaccine available.