I'll concede for now the purchasing ticket point, simply because I'm not sure how well that's used. However, we already limit ticket sales to some extent, as they're not open in the middle of the night.
Which is a completely irrelevant argument, as most transportation services have a massive dropoff in customers in the middle of the night unless they are open to do red-eye connections. Clearly, SPUD is positioning to be exactly this (against, 16th largest MSA in the United States) but aside from a mini-peak of concert-goers/barhoppers you generally are going to have a massive dropoff in activity. There is no comparison here to mid-afternoon.
I haven't even been suggesting we're only open for an hour around the window of the train...there's still plenty of time for the people who would buy tickets on-site to buy them, albeit maybe in a bit more inconvenient fashion (for example, they'll have to run over there at 4 or 4:30 pm instead of "right after work" if they get off at 3 or 3:30 pm.)
For you, an inconvenience, for others a near impossibility. You admit you're a layman and only looking at what is convenient for you. You buy tickets online in your underwear at 2am. That's great. I've worked face to face with working class people for a long time. 4:30 is when you need to head to the daycare to pick up your child or be charged by the minute for being late. And rush hour is already in swing so expect longer travel times. Doesn't look like a great time to run an errand any more, does it?
Or suppose you are a traveler. You need to get your ticket changed. You head to the station during the daytime and find out it is completely shut. How friendly is that?
However, the current Midway station can only be effectively used for Amtrak to Amtrak services (including the Thruway services offered by Jefferson Lines.) Other connections are either made at the Greyhound terminal in Minneapolis or at SPUD. Local transit doesn't even directly serve the station...it's two blocks down the road on University Ave (and it's just a flag stop.) While people may be waiting for someone to pick them up, apparently closing the station about an hour after the train from Chicago arrives is enough time for people to be picked up, because they close at 11:45 PM.
Many airports and station facilities close at 11p-12a time frame. They may even be "closed" when final arrivals come in. Final arrivals at Washington Union Station occur after the night-time curfew. People scramble out of there and cops stand around making sure you leave. No fun if you are a night owl but most of society, at least the ones who make the decisions, are on a circadian rhythm. The point you are making is true but not particularly relevant.
Furthermore, you have to look at the timing of accommodations. Most hotels want you out by 11am. So you may need to check bags during the day prior to a night-time departure. However, check-in times usually are no later than 4pm. So for business or leisure travelers there is no reason to linger after a late evening arrival before proceeding to accommodations. Make sense?
Now when college students rule the world I would expect things to be different on that front.
The point I'm trying to make is that Midway is not used for non-Amtrak connections, as no one else serves it. If it did, or it had a robust enough network that it made sense to be open all day, sure. But I don't see that with Midway. SPUD hopefully will be that way, but then Amtrak isn't the only user, and we're back to that ticketing question again.
Nobody walks? Cabs are banned in Minnesoooda? Just because the connection sucks doesn't mean nobody is attempting it. When Amtrak moves into SPUD probably this activity will increase in a massive way. MSP certainly hopes so.
However, I'm guessing Midway is not the only one in its position, and it may be worth evaluating situations like it.
You seem to have trouble grasping the fact that this is a high volume station in a top-20 MSA. You have also failed to acknowledge statements earlier by others in this thread with intimate knowledge of Amtrak staff scheduling practices. The fact is that keeping the station open is probably a more productive use of staff time than cutting hours and closing the station to patrons during that "gap" that so bothers you.