The distribution of Elo ratings will not tell you how strong the average player is in an absolute sense.

Elo ratings measure differences in skill between different players. A player rated 400 points above another player will win 90% of the time. Only rating differences are meaningful. Absolute ratings aren't.

Yes, I can understand why absolute ratings are impossible to extract.

However, since the population maintains some continuity over time (players gradually enter and then leave over time), would it not be possible to reconstruct relative ratings between players that didn't play during the same era?

Only if you were to assume that a player's prowess remains constant throughout their career, which we generally know to be false. (I'm completely inventing dates here) If Fisher played Kasparov in 1990 and Kasparov played Carlsen in 2020, you can only compare Carlsen to Fisher if you assume Kasparov's skill was about the same for this entire duration, which no one believes to be the case.

A lot of people don't realize that chess players peak around the same age as athletes do. Carlsen was at peak dominance in his mid-20s. Kasparov peaked later, at 36 years old, but still, it wasn't at age 50 or 60.

Chess requires you to be really sharp. Experience increases with age, but there's some cross-over point at which the decline in calculating speed is more important than increasing experience. Heck, I'm measurably better at chess tactics in the morning after a good night's sleep than in the evening after work.

I'm sure it's also a matter of how much time you actually dedicate daily to this - and it's quite hard to maintain passion and focus for 8+h /day on the same game for 30-40 years.