Plenty of things are left out, indeed. to add to the list of missing, important numbers:

> so if you are vaccinated you can get infected

Yes, you _can_, but at what rate compared to unvaccinated people? It's not the same, real-world data shows that.

> What's the mix of vaccinated and unvaccinated people in the hospital

This number is meaningless without also knowing what percentage of the people are vaccinated. Compare:

"80% of the people in hospital have $foo, and 80% of the general population has $foo" - $foo has no bearing at all on hospitalisation.

"80% of the people in hospital have $spon, and 5% of the general population has $spon" - $spon is clearly linked to the majority of hospitalisations.

"45% of the people in hospital have $bar, and 5% of the general population has $bar" - $bar is linked to higher rates of hospitalisation, _despite_ not being the majority of hospitalisations.

Spoiler: for some age groups in the UK now, "being unvaccinated" is much like $bar.

Headlines about e.g. the Provincetown outbreak that say "most people hospitalised here are vaccinated" without further clarification, are somewhere from meaningless to misleading.