What are these "open mics" that people often refer to? AFAIK, they don't exist here in Los Angeles and I never encountered one growing up in Florida, either.
Well, I have heard of open mics for singers or duos, of course, but never for a full band.
Is this really a thing, where a full band can play just a song or two?
Most times the only way a full band gets to play at one of these open nights is if the band belongs to the guy or girl hosting the evening.
I've seen a lot of "open" mic/jam nights where it's captive audience hour while the host's band plays a full set (sometimes more) before the first audience musician even gets asked up onstage.
Totally jive move AFAIC. But when you're running the event, you get to make those calls.
That's one of the reasons I stopped going to "open" jam and mic nights.
Note: Where I am, if it's billed as an open mic night, it almost always means just that. If you want to step up to the microphone, that's what it's all about. But the backup band is usually set in advance for those. Many times they're doing it in hopes of finding a new singer without being too obvious about it. Open jams, on the other hand, mean instrumentalists are also welcome. But the host's backing lineup still holds the stage throughout the evening. They don't often quit the stage and have a complete band take over for awhile.
It may be different in other places - so take the above for what it's worth.