Absolutely, and eventually, evolutionary pressure is to become less deadly. Doesn't do a virus much good if it kills all of it's intended hosts, but since mutation is random, you'll be going through the full range of more deadly, less deadly and no change in virulence variants over time...
Either way, vaccination to the point of true herd immunity, and we're talking into the 90% range as I've often ranted about, snuffs it out without waiting for the time it takes for it to become less virulent. This avoids millions of needless deaths on a world-wide basis, something you don't mention in your personal ramblings...