Crowbar circuits are brutal, destructive and primitive IMO. In any case, all they serve to do (with the Quad 306) is trip a circuit breaker on the primary, blow a line fuse, and often several other parts (transistors, and in earlier models, SCRs) I don't like crowbar 'protection'- it is like throwing an actual crowbar over power lines- spectacular but not very clever...
...The Japanese had it all sorted in the late 70s. They developed complete protection circuits on a single SIL IC and they are still reliably saving gear and speakers from all types of failures and abuse.
examples: uPC1237HA, TA7317 etc
If I were designing amplifiers (which I'm not thank goodness), I would be more paranoid about burning houses down, or damaging uber-expensive speakers, than what happened to the amplifier! And part of this is when circuits go faulty rather than merely operating correctly when having to handle a short or a dodgy load.
Using a series relay to protect against DC (as in the IC examples you give), for example, is fraught with difficulty, with the possibility of arcing and/or welded contacts:
https://www.halfgaar.net/dc-protection-with-relays
(They are also not for 'purists' because of the imposition of a tiny pair of partially oxidised contacts in series with their 1" diameter speaker cables!)
I don't know for certain that Quad's circuit was/is perfect but I think it shows signs of having been 'thought about' in their quest to be the manufacturer with amplifiers stable into any load and capable of being a workhorse that survived in professional environments. Like a lab power supply, an amplifier can be designed to survive an output short circuit and be stable into an open circuit. Certain topologies will prevent horrible 'thumps' at power-up without needing a series relay (e.g. the Quad 306). The amplifier can be maintained in its safe operating area (SOA) by monitoring various parameters and shutting down transistors if a certain envelope of power and time constants is strayed out of (something pioneered by Quad also, I think?).
What remains is the possibility that something goes wrong, like a transistor going faulty and becoming a short circuit, or a dry joint upsetting the bias or preventing some of the protection working, etc. In that case, you might need your protection circuit, but if it's a 10 year old relay, it might fail. The crowbar is the ultimate 'backstop'. It's a solid state device so its response time is instantaneous, and it is there to protect the load, not the amplifier. If your amp can survive a short circuit, it will not damage the amplifier (although the amp may be faulty already).
The Quad circuit also contains a circuit breaker in the power supply as a prior line of defence - faster and more precise than a fuse, and resettable (although there are obviously fuses too - multiple layers of 'failsafe'). And its other big feature is its floating ground power supply. The amplifier is direct coupled, but the power supply is, in effect, AC coupled! This limits the energy that can be dumped into the load if something goes wrong.
I would much rather be using a Quad amplifier than something designed by, say, S***t.