52-week list/year-to-day list would be something else. Nothing like that exists in chess. A top player can go an entire year without playing and will keep his number. How would you go about a 52-week list? I might be unimaginative, but I can't see how you would do anything besides "career" list this way. Unless you have all players start over - like everyone ranked 1500 at the start of the year. In which case playing lots of lowly tournaments would count unproportionally.
What looks more achievable IMO, is to post yearly movements. If player x started the year at 2800 and is now 2840, it has been a good year. But it will not be immediately apparent if it has been better year than for player y moving from 2600 to 2750.
52-week list/year-to-day list would reflect not what exists in chess, but what exists in tennis. Official 52-week list determines actual ATP/WTA ranking, which determines seeding for the tournaments. The Elo list would reflect just the same, results from matches a player played in the last 52 weeks, and whatever the numbers show from that, just with any statistics, is fine. The same goes for year-to-day list.
For me, it would be interesting to compare those lists with official ATP/WTA ranking, because official ranking favors higher prized tournaments. If we imagine the situation, for instance, that one player wins 2 tournaments, one from 500 series, and one from 250 series, playing against exactly the same opponents on both tournaments, in exactly the same number of sets, he would be awarded double points for the 500 series tournament for exactly equal accomplishment as on 250 series tournament. Elo rating system irons those differences, taking into account only head-to-head achievements.