While your need to register to vote in the first place is a little weird and backwards, anything which gets more people involved in the electoral process is a good thing.
To some extent we need to have voter registration. The thing is the right to vote isn't enough, to vote the government needs to know who and what you can vote for and since there is no general obligation to tell the government where you live it has no way to know this. I recently had to do an in-person request for an absentee ballot and that gave me a behind-the-scenes peek from listening to the employees talk. They had to take my address and figure out what precinct I would be voting in and then go get an appropriate ballot for that precinct. There were IIRC 4 (the ballot isn't in front of me) offices on that ballot in this election that are address dependent and probably a couple more that I didn't even see as I live outside the city proper--no city offices will appear on my ballot.
There are some things we could do, however:
1) We already have motor-voter laws in many places in an attempt to address this but I think they go too far--they make it trivially easy to register to vote without checking if you are a citizen. Now, a native speaker isn't going to have a problem understanding but those with limited English could easily be confused.
2) The reality is that most people do have to tell the government where they live because of driver's licenses.
2a) Rather than motor-voter, I would like to see voter registration
automatically updated when you change the address on your driver's license, or replace it with one from a new state (they have the old one, they know what registration to cancel.)
2b) I would like to see the polls required to accept anything that would be adequate to get a non-driver's ID plus something establishing citizenship as adequate for voting. (I think this would be a minor issue, though--the problem is people who don't have ID in the first place, not people with ID but no voter registration.)