I think so.

I don't even think "covid burden" was the topic, depending on how you define that it could mean the demographics most at risk hospitalization (as overwhelming hospitals seems to have been the concern, and justification for lockdowns). It was only defined as people acting as reservoirs and vectors. This is essentially the entire population given that experts believe catching covid is inevitable, and that the virus can persist after exposure, including in the gut. So the only distinction I can see being made in this context of inevitable infection, reservoirs, and vectors, is vaccine status. Which is not a great dividing line. Basically, my whole point is that in the context of reservoirs and vectors, there's not a reasonable basis for a division into two groups.

If by introducing demographics, you are referring to age: one can - and should, for various purposes - partition the population by age. Doing so is somewhat more arbitrary than, say, by vaccination status, but both can be clearly well-defined. The difference is that no-one chooses to get older, and so there are no ethical issues with it.

As for the argument that everyone will get it eventually: For one thing, the pace matters, the recent shortage of ICU beds is a negative public-health outcome, and the statistics clearly show the benefit of vaccination in this regard (few health issues have better statistical evidence.) This alone shows that there is a reasonable basis for so dividing the population.