In most actual businesses, “open until 4:30” means “we stop taking new business at 4:30, but we’ll serve everyone who was here before then, regardless of how long that takes.” Restaurants don’t always like it, but if they “close” at 11 they’ll seat you at 10:45.
There’s a good reason for this – those businesses have to care what you think. No matter what’s actually “fair,” the customer generally wins because the customer can – and will! – take their money elsewhere if they feel mistreated.
At the DMV, “open until 4:30” means “at 4:30 on the dot we go home, no matter when you got here, how long you’ve been in line, etc.”
At the organizational level, they have no reason to act differently. You have to use that service, and there are no competitors. No level of crappy service affects them in any way, so why change?
But even on a “trenches” level, I observe something interesting. When you come into a business at 5 minutes to close, the employees might stealthily roll their eyes, but they hustle. They want you out of there, so they can get out of there. 10 minutes to close at the DMV, they just stop working. They have no reason not to. They don’t have to clear out any queue before they can go home. They have no incentive, personal or organizational, to work hard.
Incentives matter, at every level. If you want a great life hack, figure out who’s incentivized to help you and seek them out. And figure out who has NO incentives to help you, and avoid them like the plague. Unless you’re forced, of course.