So it's even better for a non-citizen, because you can just turn around and go home?

I don't get why some people end up in a detention center. Why not send them back home on the next flight? Even if people can't pay the ticket a lot of embassies will immediately pay for their citizen's ticket. Especially if they have a job and will be able to pay it back in a reasonable time. If it's an EU citizen they can be sent back on any flight going to Europe. So there is usually a possibility to leave within the hour.

Most people probably won't like having their plans ruined and a bunch of money wasted being forced to abandon their travel. And the US may be home to a noncitizen.

As for why they end up in a detention center, maybe immigration thinks they might want to ask them some more question, or maybe they're just exacting some punishment on the uncooperative foreigner.