COVID-19 Outbreak Information Updates (Reboot) [over 150.000,000 US cases (est.), 6,422,520 US hospitilizations, 1,148,691 US deaths.]

That's an excellent point. I would love (and I know this

Then there is the viral load aspect.

Viral load has a huge impact on transmission, and vaccinated people who get the virus will have a much lower viral load.

So while the vaccine doesn't prevent you from transmitting the virus, it absolutely makes you a less effective transmitter when infected, by the same mechanisms that make your severity of disease symptoms much lower.
CDC data is a bit lagging but a fully vaccinated person is 4-8 times less likely to catch covid. That data is up to the end of Nov. Other sites have more recent. I just need to look.

However, is the case rate lower due to immune response and/or being less infectious? Or is it lower due to vaccinated people are also more likely to mask up, take precautions, etc?