I'm gonna keep this simple so it doesn't get too mixed up
When prestiging, it should save the player's current stats in a menu to see how far they've progressed. It would show everything on the player stats menu ( KDR, favorite weapon, highest score, etc.) but only for that prestige. You could see your stats from 0 and compare them to your current stats or one from a previous prestige.
It should still definitely retain the overall player stats with the per-prestige stats under/next to the box. By no means will this be a replacement, more like an addition to the stats screen.
Just a cool time capsule thing to go back and reflect on, nothing too major