Ok, you got me there. But -

> If you can prevent that, then you can likely limit or eliminate the spread.

That doesn't make any sense. Mitigating serious illness puts no downward pressure on transmission.

And in fact, if someone's symptoms are reduced and they don't need to test because they aren't required for vaxxed, it may even encourage spread.

I believe that is the case for covid at least. If you don't get as sick then that means the virus didn't manage to spread inside the body as much, so there is less viral material that can be spread to others. Now I'm not saying this relationship is linear, I have no clue. We'd have to ask an actual expert.

You are right that this could be offset because there is no isolation happening in case of an unknown infection.