Absence of evidence is not evidence of absence. We are discovering new long-term side effects of COVID-19 exposure everyday, most of which could have been prevented by inoculation.
As for evidence the vaccine caused medical problems, it already exists. The CDC tried to block the v-safe data from being released.[2] It shows overwhelming safety signals which the public should know about to have informed consent.
[1] https://www.thelancet.com/journals/laninf/article/PIIS1473-3...
[2] https://aaronsiri.substack.com/p/v-safe-part-1-after-464-day...
"""Although peak viral load did not differ by vaccination status or variant type, …. Fully vaccinated individuals with delta variant infection had a faster (posterior probability >0·84) mean rate of viral load decline (0·95 log10 copies per mL per day) than did unvaccinated individuals with pre-alpha (0·69), alpha (0·82), or delta (0·79) variant infections."""
Yes vaccinated with pre-alpha, alpha, and delta have faster viral clearance... but what about Omicron which is 99% of cases now? Maybe the study was done too early, but the results are very bad for vaccinated with Omicron.
"In other words: out of 100 boosted persons who catch Covid, 31 — or one-third — will be still carrying LIVE VIRUS on Day 10. Out of 100 unvaccinated persons, only 6 would test positive on Day 10 — over five TIMES fewer people." [1]
So even if you justified treating unvaccinated differently due to viral clearance (completely disregarding that prior infection, age or weight has much more influence), eventually you'd be wrong using that metric anyway.
[1] https://igorchudov.substack.com/p/study-boosted-people-slowe...
There was a paper going around not too long ago whose headline result showed there was only a mild decrease in infectiousness, something like 24% immediately after vaccination, which some thought was a gotcha all by itself but (a) that is certainly better than nothing, and (b) it was based on prisoners who shared a cell, so a fairly extreme case of proximity and duration anyway.