It's pretty simple Quince.
The problem with knockout ties in Europe is that home advantage is significant, so they invented two-legged ties.
The problem with two-legged ties is that if they end in a draw, you can't comfortably replay the whole tie.
And some other ways to split the teams are clearly unfair (extra time favours the home team at the second ground) or crappy and devalue the efforts made in normal time, like penalty shootouts.
Interestingly, it is a myth that there's an advantage to playing the second leg of a two-legged tie at home. Statistically there's no advantage.
