Channon-H2O is quite correct. Years ago it was very difficult to win the double of the League Championship title [to give it its proper name] and the FA Cup or League Cup. There is nothing wrong with either cup competition. People talk about getting rid of the League Cup, but that's utter twaddle. The reason the Cups have been denigrated is purely because, as the OP said, if the top teams seriously wanted to win it, they could, and probably without breaking a sweat. And this is the problem. The teams at the top are too big, too rich, and they only have themselves as competition, with the rest of the 86-88 teams just making up the numbers. They have ruined the competition in the Premier League, and it has spilled over into the Cup competitions. One day, the Premier League will only be a distraction, or a keep fit exercise for those clubs who just want to win the Champions League. The way to cure the problems with the Cups is to curb the growth and riches of the topmost teams. Then we'll get the proper competition back and it won't be so easy for them to win things. And then clubs will start looking at the FA Cup and League Cup as trophies worth winning again. Of course, waiting for the day when rules actually rein in football clubs will be like waiting for snow in hell. But it's what needs to be done to bring the competition back in English professional football.
Best competition in the world, being a Sunderland supporter and 1973 was amazing, hope we get there in may again!. I would rather win the f a cup than finish 4th.