I don't know the stats behind it, but I've heard from news that those with the vaccine do still host the virus when exposed and even continue to pass it along (although they experience lesser/no symptoms).
If vaccinated people do become infected at the same or similar rate to unvaccinated (and a whole lot of other assumptions), it almost seems like there is a scenario where the vaccine could be worse than the virus because we're essentially creating many Typhoid Marys that continue to host and spread the virus unaware that they're contagious, giving the virus a massive pool to mutate within.
> If vaccinated people do become infected at the same or similar rate to unvaccinated (and a whole lot of other assumptions)
They do not though. You getting sick from any virus is a function of your particular immune system, the viral load you're exposed to, the virus' infection mechanisms, and your manner of exposure.
Vaccines affect the first two points. They train your immune system to recognize the virus as something its seen before and it has ready antibodies to fight. Your immune system responds more efficiently to the virus and neutralizes it faster meaning that any point during your "infection" you've just got fewer virus particles to shed and spread to others.
If you're exposed to a high viral load you might become symptomatic, your white blood cells can only work so fast, with a breakthrough infection but since your immune system is pre-trained for the virus it'll be a shorter and likely a less severe infection than if you were unvaccinated.
The Typhoid Marys you're describing are the massive pools of completely unvaccinated people getting sick. The unvaccinated remain infected longer and end up producing more copies of the virus from their infected cells. If the virus generates a beneficial mutation (named variant) after a trillion replications and each unvaccinated person produces a billion replications (made up round numbers) then we'd expect a variant every thousand people infected. If a vaccinated person only produces a million replications then it'll take far longer for a vaccinated population to generate a variant. You may never even see a variant emerge if the infection rate drops below pandemic and epidemic levels.
If vaccinated people do become infected at the same or similar rate to unvaccinated (and a whole lot of other assumptions), it almost seems like there is a scenario where the vaccine could be worse than the virus because we're essentially creating many Typhoid Marys that continue to host and spread the virus unaware that they're contagious, giving the virus a massive pool to mutate within.