Most people who don't have a license DO have a state government issued photo ID card, or else, how could they cash their paychecks?
Seems to me if you're working "normal" hours, you probably aren't poor. Most of your service industry workers and factory rats (who I'm guessing you're referring to as not being able to afford to miss work) don't work 9-5.
BTW, I don't know where YOU live, but in Michigan, it only costs $25 for a license, and ID cards are $10. Plus, the Secretary of State (we don't have a DMV) branch offices stay open until 5 p.m. on most weekdays, until 9 p.m. one day of the week, and they even have Saturday hours.
I can't imagine too many states being less accommodating to their citizens than Michigan by having such restrictive hours as you claim. I'm also guessing that state government issued ID cards cost less than licenses in most other states.