As an American, I want people to vote who want to vote and for no other reason. They should have nothing stopping them from voting if they want to, and nothing artificially pushing them towards doing so either.
The big problem in America with voting is that election day is not a national holiday. If there should be any incentive to vote, there should be fines for employers who don't give election day off (not saying people cant' elect to work that day, but it needs to be a default holiday), or a mandated pay hike to employees working election day (say, doctors, police, utilities workers, etc that can't really have a day off).
But absolutely don't mandate individuals vote. Its their right not to. You don't get to go around telling other people how to behave if it doesn't negative impact you. And the people not voting now won't become more inclined to get involved because they are forced to, in the same way children aren't intellectually stimulated by being forced to go to public schools.
Or you could do like Washington State and change to a mail-only system. I voted weeks before Election Day, and then dropped my ballot off at my convenience.
I could see your argument for having deliberation day or something, but there are other solutions for the problem of long waiting lines at the polling place. (I was 18+ and resident in California previously, so I waited those lines, too. I wasn't employed then, though.)
No, because I believe on principle a government shouldn't control the movements or day to day actions of their population. That goes from drafts, to compulsory public education, to mandatory voting. Making education non-compulsory is a lot harder than just saying "kids don't have to go to school anymore" but I'm just giving examples.
Well then what exactly is the point of government, in principle, if they have no authority at all over people's lives? If everyone could do whatever they liked and ignore any rules set by anyone else, all the benefits of collective action vanish.