I was thinking exactly the same way , me and some friends were talking about it and there is no real champ with hand to hand style fights ( we imagined like batman or daredevil kinda thing ) there is still some champs that are close ( udyr or vi ) , at the end we said that the perfect champ would look like Jonathan joestar from jojo's bizzare adventure with those types of spells :
Q - ( work with the animations ) left fist damage buff
W- (work with the animation ) right fist damage boost
E- double fist punch with aoe or a CC or passive armor
R-Rain of punch , like a big wave while an enemy champ is CC'd
Passive : Different type of animations and combo can be performed that can change the type of damage given or if the champion is in front of all his mates and engages gains extra damage and armor