If you have a memory-constrained system, yes. There's a surprising amount of stuff that sits untouched in RAM for very long periods of time. I generally run fairly low-end systems, so it's not unusual for me to have a few GB in swap. (Though I just found out last week that I could buy another 4GB for $26 and free shipping, and I have to admit that was a worthwhile investment.)

Yes, if you have 8GB of RAM which is enough for me 99% of the time, but you'd rather your computer slow down 1% of the time rather than crash and have to start over.

Yes. You need swap to hibernate a laptop.

But is hibernate relevant? I've found suspend to be much more reliable, and good enough in terms of energy consumption (thanks to modern low-power states in CPUs).

I find it relevant. I use it to store the state my work laptop is in at the end of the day, and then restore that state when I get back to work the next work day. That way I don't need to keep it switched on when I'm not using it/transporting it.

Is there a better solution to this other than hibernating?

Duh, yes, that is needed. I don't have hibernate enabled on my laptop though, nor more importantly, my server.