It's not silly at all. Many populations have difficulty maintaining current state-issued IDs with current addresses displayed on them. Remember that voting is a constitutionally guaranteed right. Driving is not. ID is not.
Example: Your mother falls and breaks her hip, requiring that she move into an assisted living facility in a neighboring town. How does she get to DMV to get her state-issued ID updated?
Example: You're a chambermaid at a hotel, which requires that you work from 5AM to 4PM daily. You don't own a car and you don't get PTO or paid breaks. DMV is open from 8-4, closed from 12-1. Your 1-year lease wasn't renewed and you had to move recently. What do you do?
You also have the issue of right to vote. Municipal elections in my city require residency, not citizenship. How do you distinguish between these elections?
Voter-ID proposals sound reasonable and neutral, but only exist to increase the friction associated with voting to decrease voter turnout, particularly among the poor, elderly and minorities. Just like Amazon has one-click to increase conversion, and eats the cost of accidental orders, the voting system needs to be as frictionless as possible for a strong democracy.