First of all, in most countries an expired proof of citizenship is accepted for many purposes because it's assumed that people didn't go out of their way to coincidentally lose their citizenship or permanent residence when the ID expired. If it proves residence or driving qualifications, then there are certainly other reasons why it should expire.
Suppose we have an administration, decentralized or otherwise, that stores the records of the people concerned. They can then be contacted and details can be verified.
This informal verification already occurs on many levels, particularly in the US due to the lack of consistent ID. Try flying on a flight without photo ID, entering the US as a US citizen without proof of citizenship, etc. You will be permitted to do so with a bit of extra hassle while you're identified to a reasonable degree of confidence.
edit: To get an EBT card in NYC you can do it all online if you have a valid (ie, not expired, ID card.) If you do not have a valid (ie, expired, ID card), then you have to go to the DMV so they can take your picture and you sign a few forms. The forms are available in 22 languages. At the same time they may work to get you a new, valid, ID card.
How is this unreasonable?
1) You have to go to the DMV office
2) You have to agree to have your picture taken
3) You have to fill out 3 forms (offered in your native language -- 22 languages are offered)
4) You have to provide a mailing address for where the EBT card will be sent
And then you have to be on the other end of that mailing address to receive and activate your EBT card.
This all seems like very easy procedures to follow to get food stamps.
No it isn't. The marginal costs are different. If you earn $2000 a week and through some mischance have to give up a day's earnings to go the DMV your $400 loss is an annoyance. If you earn $500/week your loss as a percentage of income is the same but the economic impact of losing $100 is probably much bigger.
That’s reality for millions of people.