Would also point out that even non-political and voluntary cost recovery, such as poor counties soliciting donations at the polls to help cover the cost of ballots has been barred as an unconstitutional poll tax.
Again, your idea is not new and has already been shot down.
Again, I don't see it as a tax as no one is charged any money if they abide by the law, which is that citizens with documentation can register to vote without being charged fees. Free. Many government offices charge fees for processing documents and searches, that is nothing new. Try getting a copy of a birth certificate. It's a service fee, not a tax.
Additionally, just because a certain procedure is in place does not mean it is right or valid. What comes to mind is people voting without any checks of their validity to vote per the law. California has taken it a step further by allowing illegals to obtain drivers licenses without checking legal documents. It may be current procedure, but is not right.