If you believe "the side-effects are well studied and well known" let me point out some other drugs where the same was claimed and many died before they figure it out.
Thalidomide, 1961
Diethylstilbestrol (DES), 1971
Aventis: Terfenadine (Seldane) 1997
Wyeth-Ayerst Laboratories: Fen-Phen, 1997
Roche: Mibefradil (Posicor) 1998 (bad drug combos)
Warner-Lambert: Troglitazone (Rezulin) 2000
Phenylpropanolamine (PPA) 2000
Bayer: Cerivastatin (Baycol) 2001
Merck: Rofecoxib (Vioxx), 2004
Pfizer: Valdecoxib (Bextra), 2005
Able Laboratories Generic Prescription Drugs 2005 (bad manufacturing)
How do you know "the answer is yes, by a long shot"? You believe enough time has passed to determine that?
Let me be clear, I am NOT arguing that the vaccine wasn't "safe". Or that it has serious side effects. I am only arguing we just don't know the fine details yet, that there may be cohorts to which the vaccine was/is not worth taking.
Time will tell. Instead of accepting that we don't know yet you double down on your statement that the vaccines are perfectly safe. If everyone had that attitude then people would still be dying from the drugs above.