Except that all the existing evidence suggests your argument is backwards. Whilst Covid-19 vaccination doesn't provide full protection for either the vaccinated or those around them, it seems to be much more effective at protecting the person being vaccinated against severe symptoms, hospitalization and death than it does at stopping them catching and spreading the virus to others. As far as I can tell, literally the only reason vaccination is primarily framed as a way of protecting others is because that framing fits better into left-wing politics; it has nothing to do with the actual evidence.
According to the CDC, each vaccine efficacy at preventing the recipient from catching the virus. To your point they also reduces severity of symptoms. Looks like the J&J one ain't that great at prevention.
Based on evidence from clinical trials in people 16 years and older, the Pfizer-BioNTech vaccine was 95% effective at preventing laboratory-confirmed infection with the virus that causes COVID-19 in people who received two doses and had no evidence of being previously infected.
Based on evidence from clinical trials, in people aged 18 years and older, the Moderna vaccine was 94.1% effective at preventing laboratory-confirmed COVID-19 infection in people who received two doses and had no evidence of being previously infected.
The J&J/Janssen COVID-19 Vaccine was 66.3% effective in clinical trials (efficacy) at preventing laboratory-confirmed COVID-19 infection in people who received the vaccine and had no evidence of being previously infected. People had the most protection 2 weeks after getting vaccinated.
That's from the clinical trials, which are like two variants behind what people are actually being exposed to in the wild right now. The vaccines are much less effective at preventing people from catching and spreading the currently-circulating Delta variant than the original one which those numbers were based on. Firstly, they don't stop people from catching the virus nearly as well, and secondly vaccinated people who do catch the virus seem to have comparable viral load and spread it just as well as the unvaccinated. Also, the Delta variant is just better at spreading in general, which itself means a more effective vaccine would be needed in order to prevent everyone from inevitably catching it.
It's more nuanced than that. Prior to the delta variant, there was strong evidence that the vaccines also prevented you from being a carrier of the virus in most cases.
The calculus with delta is different, as it does seem that vaccinated people can spread delta. But the severity of that spread, as well as the amount of time a vaccinated person can spread it, is certainly lower than that of an unvaccinated person.
