What about the old gym adage "training to failure is failing to train" - is there any physiological basis for this, or is it mental, or just a myth?

That’s a Pl/Oly mindset rather than a BB/hypertrophy mindset. Totally valid advice in the right context.

Long story short, failed reps get much more risky and problematic as the weight you’re lifting approaches your 1RM.

not an expert, 2 years of serious lifting, but this is probably a good adage for the average person from my current understanding

training to failure puts you at higher risk of injury and there are diminishing returns as you approach your 1 rep max and/or failure

hypertrophy can happen with more reps or more weight

strength gains are usually just focused on progressive overload

though, of course, hypertrophy will happen either way and contributes to increased strength, but this seems to be further confirmation that you can gain muscle size either way

It's definitely way more nuanced than that. You have to approach exhaustion to get the body to eventually build strength. But you need to carefully time your rests/deloads and handle plateaus with more volume.

I’ve never heard that, it’s usually the opposite- people do strip sets and the like to reach failure