Oh, absolutely! But it’s not really a mammoth campaign so much as four ways to play. The whole point of the game is to finish a run with your choice of character, weapon, and cards.
There are four “runs”, or acts, available in the game, and some of them share the same levels, but they’re all mixed up by the corruption cards and director actions. If you want to fast-forward past the early levels, I think that’s the purpose of the later acts. They’re harder, so they start you off with more cards. In fact, Act IV is just a big boss fight with all your cards in play. But I will gladly play through any act again just because I’m enjoying the synergy among four dramatically different variables: 1) the people with whom you’re playing, 2) the character you’ve chosen, 3) the weapon you’re using, and 4) the cards you put into play. And I will gladly keep playing Back 4 Blood, not to get through any sort of “mammoth campaign”, but to try out the various combinations among those four factors.
And to unlock more cards, of course!