This is actually the way Oregon does it. You don't mail it back, there are dropoffs (located all over the place).

You are also automatically registered by default, but can elect to opt-out.

https://en.wikipedia.org/wiki/Vote-by-mail_in_Oregon

It's pretty convenient. (I live in Oregon.) Dropoffs are all over the place, you can do it right up to the end of the day on election day, but really you have 2 weeks to fill it out and drop it off.

I believe it's resulted in Oregon consistently having one of the highest voter turnouts, which is notable, since there's next to nothing spent in the state in terms of campaign advertising, and the senate races are not particuarly contentious.