To get the rate one can indeed calculate it with smaller representative sample, but that just doesn't imply that the vulnerable people would somehow never become infected if the epidemic continues, so the deaths of the old can't be avoided then. That the old die much more is a fact, and nothing that by itself "exacerbates" the rate.

Edit: I haven't seen any argument that estimated more than 20% of NY population that were supposedly infected were somehow specially skewed sample to hit only old people, and I'd argue that if the sample is that big it's quite improbable. If the argument is that the virus got faster in the nursing homes, one can also argue that all the old people outside of nursing homes skewed in the another direction by managing to initially not get the infection, but that as epidemic progresses they would indeed eventually become infected and suffer.

Edit2: "the virus is rather showing signs of going away" claim is very curious to me. I don't see it "going away" looking at all the statistics across the different parts of the world. I see only the slowdown of the spread, which corresponds to people generally changing their behavior to slow it down.

If it is the case, you don't expect the same death rate to scale up as the wider population continues to get infected (if it is still happening, the virus is rather showing signs of going away).