That's a good answer, and consistent with this very good article by Johns Hopkins epidemiologist Justin Lessler. He makes many of the same points you make, and adds that there will likely also be partial immunity even within individuals. (At least, I suppose, if we aren't facing antibody-dependent enhancement.)
Here's a credible-seeming claim from a computational biologist that, if COVID-19 is like other coronaviruses, long term immunity is unlikely. I imagine this also means a vaccine is unlikely.
If true, this changes everything. Does this mean we are all going to be working from home for the rest of our lives? Or will we accept a world where there is an endemic disease that we get for 3 weeks every year?