Your friend is right. This is an idea that gets suggested a lot and it will almost definitely never, ever be implemented into league.
Simply put imagine this scenario:
You walk up to a Lux. You think 'oh I can dodge her ult no problem!' then suddenly she suppresses you with a Malz ult. You had absolutely no idea that was going to happen because literally EVERY OTHER CHAMP has only 1 set of abilities that don't change.
Not to mention the animation nightmare that would exist in having a champ who can cast any other champions abilities. Seriously, imagine say Rumble being animated to sue Renekton's Slice and Dice. It would look like a mess.