The reason we won't need yearly vaccinations as with the flu shots isn't a property of the mRNA vaccine, it's a property of COVID-19. The watered-down explanation is that this particular sort of virus simply doesn't mutate as much as the flu virus because it has a mechanism that prevents it. We do see variants, but they're actually quite similar so the same vaccine still works (thankfully).
It's also why we're talking about COVID "variants" and flu "strains". In this context, a different "strain" usually signifies different surface proteins, i.e., you need a different vaccine for it. I don't believe that we've seen a second COVID strain yet.