That's basically how we treated butter while I grew up. So long as it's salted, it rarely goes bad outside the fridge. We had a butter dish and that was about it. The cover keeps the butter from turning a darker yellow and drying out. But we'd still eat it even when that happened.

Gotta be honest, though, I'm not a fan of grassy dairy products :). I had dairy cows growing up and in the spring their milk definitely took on a distinct grassy flavor. I personally preferred it more when it was primarily hay flavored. Store milk tastes like basically nothing in particular.