It really depends on what you plan on doing. I don't imagine anyone is asking for a music degree, unless you're going to teach lessons, or fight 300 other people for a shot at that orchestra seat, playing triangle. Within the context of other situations, such as a rock band, kicking ass is the criteria.
Focus on the kit only might be okay, but it is limited focus, and you may end up neglecting other areas. To quote Johnny "Vatos" Hernandez,
"Drummers that are just drummers are very annoying." What he means is that it's important for drummers to have a concept of other instruments.
Source of the quote, with additional context.
When I went to University for Percussion Arts, things went WAY beyond drums. My required classes included string bass, piano, marimba, music theory, ear training, notation, etc.
You might wonder when the hell anyone is going to ask you to play piano or string bass. But it's all about having that concept, because then you can play and write in a sympathetic manner that makes the other guy sound good, while being more musical.
Music theory can also improve your ability to communicate with other musicians, and it has helped me, especially in the studio, where time is money, and I'm serving as Music Supervisor for an album. Communicating quickly with studio musicians is key, when time is money.
I'm getting a bit of a refresher in Music Theory with my guitar instructors, and will be getting a major refresher in September with a composer who earned his Masters in Composition under Frédéric Durieux, and a prix d’analyse under Claude Ledoux. I'm expecting my brains to leak out of my ears.
But even if you don't have to use the actual names of things, you can still lean on the concepts.
I guess the short way to describe it is "well-rounded."
Also, lots of drummers end up becoming producers, and having an ear for all of the instruments, as well as the knowledge, is certainly a leg up.
Whenever I hear that joke about, "Who's the guy who hangs out with musicians? THE DRUMMER!" I tend to laugh, but for a completely different reason. I'm convinced that, in most cases, the drummer is the most musical person in the room.