> for a week or two
And how do you arrive at that figure? You cannot possibly have arrived at it by any principled means, because...
> Disease spread is an exponential process
Indeed. And because it is an exponential process, decreasing the rate of spread will not result in a fixed delay for all infections, it will result in a decrease in the exponent. Some people will get it a week later than they otherwise would have, some two weeks later, some three weeks... and if you reduce the exponent enough, the result will be exponential decay rather than growth, and some people will never get it at all. And even if you don't get to that point, reducing the exponent can make the difference between hospitals having enough capacity, and being overloaded and having people dying in the streets and having to rent refrigerator trucks to store the bodies.
Furthermore, vaccines are dramatically effective at reducing the rate of severe illness and death, so even if everyone gets infected and even if they get infected as quickly as they otherwise would have, you still have fewer people dying from covid, and you also have fewer people dying from other causes because the hospitals are overloaded with covid patients. That seems like a win to me.
> > The rate of spread matters a lot.
> That is a different argument
Different from what? Your original claim was there is no societal benefit to vaccination, only an individual benefit, and that is just plainly false. One of the reasons it is false (but far from the only reason) is that lowering the rate of spread has societal benefits in and of itself, even if everyone eventually gets infected anyway, and even if there were no other benefits, like reducing the risk of serious disease and death.
BTW, there are more logical holes in your argument:
> Most people I talk to had COVID and caught it off a vaccinated individual.
Well, of course they did. That's because:
> it is impossible for it to be the vaccinated. There aren't enough of them and they've been locked out of a lot of places where superspreader events are happening
If you isolate all of your unvaccinated population, then of course all of the transmission is going to happen among the vaccinated. The vaccines aren't perfect. That doesn't mean they confer no public-policy benefits. They clearly do.
Honestly, the quality of your reasoning is comparable to a flat-earther.