The challenge idea is so short sighted imo, just a lazy suggestion because other sports have it but doesn't consider how the game of football actually works in practice where a minor decision can become a major one depending on what follows.
Would you waste your 1 challenge on a throw-in that you thought was yours? Unlikely. But you'd want to challenge it if the ball was in your net 10 seconds later. How would that work? Do you have to challenge at the time, and lose the challenge once the ball is back in play? Or can you challenge based on what happens after it?
And what happens if you challenge for a penalty for Alli's handball? It clearly hits his hand. Do you lose the challenge then?
Farce is exactly what it would become, very quickly.