In praise of unfairness
A league is a fair instrument. It measures teams over enough fixtures that luck mostly cancels out, and the club that finishes first is almost always the club that deserved to. That fairness is admirable and it is also why a league rarely produces the sport's most memorable single nights. The cup does the opposite: it takes one evening, hands it to whichever side copes better, and refuses to hear an appeal about the balance of play over the season.
People call that unjust. It is unjust, and it is the point. Without it, a club three divisions down would never have a chance to beat a champion, and the sport would lose the only mechanism it has for that.
The rotation argument
Big clubs are criticised for fielding weakened sides in early rounds, and I understand why coaches do it — the league pays the wages, the fixture list is unforgiving, and nobody is sacked for a third-round exit. But a competition sustains itself on the seriousness with which it is treated, and a club that repeatedly signals the cup is beneath it should not be surprised when the eventual defeat is enjoyed by everyone else.
The clubs that take it seriously tend to be the ones for whom it is the realistic route to a trophy. That is not a coincidence; it is the competition working exactly as designed.