Wow. Purging voters from the rolls is not a felony? I'd say willfully purging a voter from the rolls is just as morally wrong as voting double.
In the Netherlands it's even easier.
From the moment you are 18, you are automatically on the register for elections.
Whenever an election is held an election pass is send to your main address.
Then only thing you have to do is show your election pass with one of the prescribed ID's (passport, ID-card or drivers licence, which must be not more than 5 years past their end date) to be able to vote.
And that ID is no problem as you're required to have one and carry it on you anyways.
There are some rules concerning when you want to use a voting place other than the one on your election pass, but even there the intention is to make it as easy as possible for all to vote.
IIRC, for national elections there are no rules at all for that. The last few elections, there was a polling place at Utrecht train station, the central railway hub, for the benefit of commuters.
That's very easy as well.
The difference is more that here every citizen over 18 automatically is registered.
The only exceptions are when your voting rights are taken away by a judge (can only be done when convicted for a crime that entails at least 1 years of imprisonment (and is not automatically so, but not sure about that last one)).
Yes, the judge has to explicitly take away your voting rights in his sentencing.
Legal aliens also can vote in county elections (but not for the larger elections) when present in the Netherlands for at least 5 years.
Municipal elections is the correct term (levels of government: municipality - province - national - EU).
In the Netherlands, the government very likely knows where you live. As I recall, you register with the local town when you move there.
It's not at all similar in the U.S. in my experience. We're a little leery of that sort of oversight. Property taxes aside, ain't nobody's business whether I live here or there.
Yes, that's right (and I don't write this to provoke a discussion on it). All residents are registered at the civil registry. Each municipality has a register with a national copy. Interested parties, such as pension funds or the tax office, get automatic updates. It's something we inherited, with most of the rest of continental Europe, from a Corsican corporal.

When you move, you go to town hall and tell them you're moving out and tell them the new address and you're automatically registered at the new place.
As to students: they're free here to register at either place, their parents' or their student's room in their university towns. University towns here love it if they register there, because the national government gives the municipalities money based on the number of inhabitants.
Voting by mail is a nearly ideal way to increase voter participation, and eliminate all the problems associated with traditional methods: inconvenient poll hours and locations, long lines, hackable voting machines, restrictive ID laws, etc. I'd like to see it adopted more widely. But you still have to decide where you live.
There's a principal problem with voting by mail. Voting is supposed to be free and secret. With mail-in votes, you don't know if someone held the voter (literally or figuratively) a gun to their head while filling the ballot. At a polling place the "free and secret" part is assured through the oversight of the pollsters.
The issues you mention with polling places are really constructed problems. Long lines? Open more polling places or make more polling booths available at the existing ones. My city of 150,000 inh. has ca. 100 polling places. Inconvenient hours? Open them longer. Here, polling places are open from 7AM to 9PM. Hackable voting machines? Abolish them or demand thorough certification (on the level that the software is provably correct

). ID-laws? I'd think that by now there would be clear guidelines on what is acceptable in that area and what not.