Automatically purging voters who have not voted in several years and do not respond to a mailed notice isn't unreasonable.
First off, cross-referencing dead people is hard, for the reasons I already explained to you.
Secondly, automatic purging
ALREADY HAPPENS. Look at what you said:
"voters who have not voted in several years"
Elections tend to be run every other year, and most people only vote every four years. So it is easier to talk about "cycles" not years, unless for some reason you are voting every year in your state.
So that is the first thing you need to understand about elections - they don't happen every year. At best, you get to find out whether someone is an active voter every two years.
So if we make it "two election cycles of non-voting before removal" that means that dead people are going to stay registered to vote for two years, and then be removed before the sixth year after their death.
That's a lot of dead people you want to keep registered, Mr.-X.
How about two years? Is that okay with you?
Well, there's no way to measure "every two years" since elections typically only are scheduled for every two years. (sure there are runoffs, special elections, and other stuff, but scheduled elections tend to be every two years)
If you make it
TWO YEARS then what you are saying, on a practical level, is that everybody needs to re-register every time they vote in a US Congressional election.
If you make it longer than that, then you are going to have to deal with the fact that there are more than two years worth of dead people who are on your voter registration list.
So, tell me, in your state, how do they do it?
Or, pick the reddest state you can find, say, Utah. How do they keep the dead people from being registered to vote there?