SS blades will also lose their edge, 'just sitting there.' It just takes longer for corrosion to get to them. But I very much prefer carbon steel broadheads. Knives too, for that matter. Much easier to sharpen to a very keen edge and the edge can take a lot more abuse than I've seen with stainless.
To fight off corrosion, I smear a little vaseline on my freshly sharpened edges. I've stored some freshly sharpened heads by coating them with vaseline and wrapping them in kitchen plastic wrap. After a year, they were still hair-popping sharp. During the season, I check my broadheads each night before hunting and touch up any that need it. I'd do that even if I were using SS blades. Just part of my pre-hunt ritual.