One would sincerely hope good condition modern valve amps would be perfectly safe, i.e. have full and well-designed fuse protection. I’m sure most are, though I’m very wary of some Chinese models that are obviously only designed for 220V and run dangerously hot (e.g. grey-import Ming Da which very regularly blew up).
Vintage amps are as good as the specific servicing and condition. They wouldn’t have lasted 50-60 years and still be highly prized if the designs weren’t sound, but manky old caps, resistors etc can be dangerously off spec if original. Even though rebuilt to an OCD/perfectionist level I’d not leave my Leak Stereo 20 unattended for longer than a quick toilet break (where I can still hear it) as the fuse protection on these is pretty rudimentary and whilst they are reliable if they do go wrong they tend to go wrong pretty fast! By saying that they were designed to be stuck out of sight in a wooden ‘radiogram’ type cabinet and countless numbers seem to have survived to this day. Anyway I’m rather paranoid about making sure the Leak is off after I’ve stopped listening.
Back when I had a little Decware Zen SET in my TV rig I did twice forget to turn it off, once I left it on over night, the other time I actually went out shopping! No issues and it was well fuse protected so I assume it would just have popped one if a tube failed. Its one reason I got rid if it, I want something far simpler on TV duty so I’m currently using a little Amptastic T-Amp which I often leave on for most of the day.
Anyway I’d expect anything decent and fairly recent (Audio Research, McIntosh, Conrad Johnson, Audio Note, Luxman, Leben etc etc) to be perfectly safe if in good condition and stuffed with decent valves.