The whole point of the FA Cup is that everyone can take part no matter which division you're in and anyone could in theory beat anyone. You're not getting that elsewhere, and in a world where the Prem, La Liga, Bundesliga, Serie A, CL dominates it would be sad to lose that.
If an FA Cup win meant a guaranteed CL place then youd'd change your tune and you'd be interested in it. They need to give the 4th CL place to the FA Cup winners - competition would gain its relevance again and talk about being fatigued would go out the window. The League Cup can get binned - it's a pointless competition at this point.