Royal Carriage competes with other 5s less than you'd think, because it basically is another one of those same 5s. After the first you'd rather just have another RC unless it's part of a multi piece engine.
In games where you want to play an Attack early and as much as possible, Royal Carriage is nearly always better than a second copy of the same attack. Royal Carriage can't collide, it can be used the same turn you play it, and it can be saved for future turns if need be. It's almost strictly better than Throne Room because of this, and it is a lot less risky and more versatile.
You know how the first person to collide KC and Mountebank basically wins? It's a lot easier to get 2 RC's on the mat, then play Mountebank and call them, than it is to buy KC in a Mountebank game and then collide them. Same basic thing applies to any number of other attacks, like Torturer, Saboteur, Ambassador, Sea Hag, etc.
Royal Carriage is just super good a lot of the time. Winning the RC split is a factor in more games than you would think!