The question would be if vaccine followed by covid infection produced more or less spike proteins (and overall health impact) than no vaccine followed by covid infection.
If you assume that hospitalization and death is correlated to overall quantity of damaging spike proteins then the default assumption would have to be that vaccines are highly beneficial.
The answer is "most likely more" given the IgG4 class switch. ( https://www.science.org/doi/10.1126/sciimmunol.ade2798 )
This is a "stand down" class for allergens, so your body doesn't overreact.
This is a similar mechanism which viral-vector vaccines use as well.
This is quite unlike regular protein-bolus vaccines which do in fact just inject a bunch of antigen into your body.
Of course in all cases, intramuscular injections don't really enter the bloodstream anyway: the immune system picks up the injected material and it is transported by the lymphatic system to be presented to the various immunological systems.
Contrast to general viral infection where a self-replicating virus with machinery specifically intended to ensure it is packaged and secreted from infected as a viable infectious agent will basically run rampant until an immune response mounts...at which pointy our blood actually will be full of pieces of spike protein from your immune system shredding virus particles (which is why PCR tests can detect infection for weeks after you've cleared it).
What about this recent study, which shows spike protein AND spike mRNA can enter the cell nucleus via a nuclear localization signal:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9909199/
What is somewhat disturbing about that, is that if spike mRNA (from the vaccine OR the virus) enters the nucleus, there are other studies showing it can be reverse transcribed possibly via LINE-1:
https://www.pnas.org/doi/10.1073/pnas.2105968118
That would mean host genome integration (DNA).
That would be bad.
Note this is no fly-by-night study, that's an NIH/NIAID/UND study.
Most notably, the plasma of patients with postvaccine myocarditis had “markedly elevated levels” of free spike antigen (33.9 ± 22.4 pg/mL), with the protein circulating in the body unbound by antibodies. “Although postvaccine myocarditis clinically occurs more commonly in males, [this] was seen equally in both affected females and males,” the investigators point out.
[1] https://www.tctmd.com/news/free-spike-protein-mrna-covid-19-...
> A notable finding was that markedly elevated levels of full-length spike protein (33.9±22.4 pg/mL), unbound by antibodies, were detected in the plasma of individuals with postvaccine myocarditis, whereas no free spike was detected in asymptomatic vaccinated control subjects (unpaired t test; P<0.0001).
So what we have is a potential explanatory mechanism (namely, probably some biochemistry which means for whatever reason these people seem to release the protein rather then keep it cell bound - although correlation is not causation, the whole effect could work the other round).