Cheap Bluetooth might have connection hitches

Fair enough, but I’ve only ever seen this happen with cheap wireless cards / chipsets that do both Bluetooth and WiFi and don’t properly avoid interference between these two (for example, I can get perfectly functioning Bluetooth audio out of my laptop with shitty Realtek wireless card if I completely disable WiFi (not just disconnect)). I think this is less of an issue for dedicated Bluetooth devices.

Bluetooth doesn’t work with airplane mode although I think most airplanes these days aren’t actually affected or we’d have planes dropping out if the sky daily.

Yeah, that’s true. As for the second part, AFAIK there was never an issue with 2.4 GHz radios (which is the frequency band Bluetooth uses) interfering with planes, it was more of a liability / laws thing - the plane manufacturer never explicitly said that these radios are safe (so the airline just banned them to be safe) and/or laws didn’t allow non-certified radios to operate on planes.

Also, does Bluetooth get saturated the way WiFi does?

Eventually yes, but it’s much more resilient than WiFi - 2.4 GHz WiFi only has three non-overlapping channels to work with (and there’s a whole thing with the in-between channels being even worse for everyone involved than everyone just using the same correct three channels that I won’t get into), while Bluetooth slices the same spectrum into 79 fully usable channels. It also uses much lower transmission power, so signal travels a shorter distance. And unlike WiFi, it can dynamically migrate from channel to channel (in fact, it does this even without any interference). 100 people actually seeing each other’s devices might be a problem, but I don’t think that’s a realistic scenario - Bluetooth will use the lowest transmit power at which it can get a reliable link, so if everyone’s devices are only transmitting over a meter or so, there shouldn’t be any noticeable interference on the other side of the plane.