So I get that I would probably memorize the damage 
does at each level eventually, but could we get an icon like 
for that shows our damage at each level? And maybe something similar for 
, 
and 
? And could we get 
in Summoner's Rift is some form? Or would that be busted?
Wouldnt necessarily be busted, but it would be very cluttered. This comes down to a personal choice. The damage numbers don't change each game, so if you know the smite damage at level 15 (850) one game, you know the smite damage at level 16 in every game. Its the same for idea for ignite.
Sure Riot could give these indicators to everyone, Or you could take the time to memorize them and be that one step ahead of them. One of the reasons I have a really good smite steal ratio is because I know the enemies smite damage just by looking at what level they are. Its really a matter of studying:P Which sounds lame in a video game, but if you aim to be competitive, then knowledge is power. Study champs, abilities/summoners damage, minion/jungle monsters damage.
also, was removed from summoners rift in season 5:D
