Yeah. I initially said leaderboard because it's the standard way of letter people compare scores that also accomplishes what I'd personally like. I don't use leaderboards like most people. I scroll down quite a ways through them to get a sense of what counts as a high score, not necessarily the best scores, and a sense of the curve of scores so I can roughly estimate how I did. A simple Daily Average accomplishes what I want far better, although I'm sure plenty will still want to know they got the best score possible.
Although ultimately I advise you not introduce anything that goes against what you personally are trying to accomplish with your game. Don't muddle your game by taking every person's suggestion in a doomed attempt to appeal to everyone. Daily Average would make the game more appealing to me, but if you want to avoid making players feel pressured, then you might want to say screw what Enchessency wants haha.