I haven't seen compulsory registration discussed on DU but I seriously cannot believe the mess of a system you've got.
Here in the UK, in late summer, the local authority sends round a form to EVERY householder. It gives a list of those currently registered for the address - you have to cross out any that are no longer resident, add any new residents and/ or children aged 16+ who will become eligible voters during the lifetime of the register OR sign a declaration that there are no eligible residents (eg all foreign citizens). Not returning the registration form is a criminal offence (although it is pretty much unheard of for anyone to be prosecuted - if you were, it would probably be a fine around £1000). Some people slip through the net - mostly people in insecure accommodation and those trying to avoid creditors - but probably less than 5%.
Next, a provisional register is published to allow any challenges/ mistakes to be corrected. The final register is published in February. There is provision to add your name part way through the year, but if you do so within a month or so before an election you will not be allowed to vote at that election.
When we have an election, polling cards are delivered to EVERY voter. They give the address and a map of the polling place to use and your registration number. The polling card is your voting ID; you don't need it to vote but if you can't show it you may be asked for alternative ID. When you receive a ballot you can watch your name crossed off the list.
Finally, just to mention that our PAPER ballots have a reference number matching the counterfoil so the ballot can be traced back to the voter. Obviously the elections officials wouldn't match the vote to the voter unless it was a fraud investigation, but it can be done.
Why not have our system? It was brought in because of widespread electoral fraud up to the 19th century and IT WORKS. Unfortunately, there have recently been experiments with "all postal
voting" which is ripe for small scale fraud on the part of individual canvassers and carers of the elderly "helping" people vote. Before, there were restrictions on who could have a postal vote - you had to apply by a deadline before the election stating that you would be away from home. So, have our system but forget about all postal voting.