On the other hand, I haven't yet had a job where written communication wasn't important from virtually day one. You may start out thinking, "Oh, I'm just going to code," but in reality you have to talk to clients (even if they're your coworkers), your bosses, prospective hires, etc., and this often takes the form of written communication. If you write unintelligibly to a customer or your CEO about why a feature is taking a while to implement, you're going to have a bad time. If you issue a poorly-worded question to a prospective hire, you'll muddy the waters in an already difficult decision. And there's no substitute for dodging the heat with a well-worded CYA email.
Learn to write precisely and concisely. Rhetoric classes, if your uni offers them, are a great investment.
75% or more of what you learn is going to be obsolete or not needed in your career. The problem is you don't ever know which is the 25% you'll use. That may even change over time. And those English/Comms classes are helpful while still being less of a PITA than your other coursework so they prevent some burnout. The most fun classes I had were a Foreign language which was taught by an actual native speaker, and a Comms class which just had a nice mix of students.
I'd say the important thing to do is to really see what is and isn't necessary. At my college, it was very common to skip prerequisites and so on. My favorite class as a sophomore was a graduate applied mathematics class where I skipped both prerequisite undergraduate classes. At first I'd assumed from the course catalog that it wouldn't have been feasible and didn't even bring it up with my advisor, but then a couple of friends pointed me to it.