Yeah, that's what I tend to do (and, gah, I never actually learned how to write a formal letter in school :/ Thankfully they're kind of like US business letters.)

It strikes me as weird that in German it's considered rude to be more casual, because here, more casual is considered friendlier. If you're writing a cover letter for a job application, you want to be formal, but after a few rounds, you can drop the formality, if that makes sense? It depends a lot on context, too.