Why stop there? Perhaps government employees should go door to door and record my vote for me. Sending something in the mail is unreasonably difficult.

Because this would actually save the government and thus taxpayers 100+ million dollars a year?

A change of address is informing the government you moved and happens millions of times a year. Automating it doesn't just save citizens 10’s of millions of hours per year it also saves all the effort by all these different agencies when people communicate the same information to multiple agencies.

Would it though? The agencies are at different levels - local vs. federal. In addition, you are notifying the post office you have moved, not the government. Your federal notification is basically to the IRS, and not everyone pays income tax, so integration there would not work. Also, not all taxpayers are eligible to vote - another complication.

You have oversimplified the details of this sort of integration and conflated local vs federal institutions. The best way to do this change would be through your state's BMV/DMV, and many states already update your registration (or offer to) when you submit an address change there.

Registration and voting are easy and well documented in every state in which I've lived or researched.

Federal and state agencies communicate all the time. It’s much easier going from the federal level down to the state level and local level.

It’s not that it takes a lot of effort per person to update the DMV and voter records it’s dumb specifically because most government agencies are automatically updated. So essentially this is just wasting 330 million peoples time for absolutely zero benefit.