I've been leveling up my impression a lot as of late thanks to the lioness quest, but I'm always just a bit sad that once I'm past Dreamboat, the game doesn't keep track of how many times you "upped" your impression.
Mostly just something for fun, there wouldn't be any real purpose behind it besides seeing how many times you've leveled up your impression beyond Dreamboat.
I think it should look something like this, where you have the number of times after receiving Dreamboat you've leveled up your impression:

This wouldn't contribute to anything apart from say, friendly competition or a neat little counter for yourself.