I believe Australia actually does this, so it's not just some crazy crackpot idea.
There would never again be an issue with "turnout."
Absolutely not. I have a right to vote or not vote. My choice.
You could always turn in a blank ballot, or a "none of the above" option if we made that mandatory, but I think it would be preferable if everyone had to at least turn in a ballot.
Wouldn't it be more satisfying anyway if you were trying to make a statement by not voting to turn in a blank ballot? This way your "vote" would be included in the count and someone would see your statement.