This topic is really interesting to me. Since I've begun the game recently, I will be able to try the E4 of each region and see if they are really that hard. I will also try to use everytime a team that doesn't contain "overpowered" pokemons.
Elite Four should be difficult and a real challenge. It's the main purpose of the league to test your abilitiy in battle.
I don't know if the actual Elite Four is too difficult, I will let other be judge of that but I don't want to have to face a weak Pokemon League.
I don't see why we should sacrifice money & Battle Points since they are giving to us after beating every member of the Elite Four and the Champion or Ghetsis. We just need to have no cooldown and there is no reasons to not getting it.
Just like others before me, I think removing the cooldown timer of the storyline Elite Four should be a thing. Since you got the rewards (Cash & Battle Points) after the final victory, I don't see why this would hurt the economy.