I believe the thinking is more that you're taking an injury risk that gain you nothing compared to stopping and resting, and doing another set once recovered if you want more volume.

Because injury will set you back far more than missing out on a few reps.

Certain breakdowns of form certainly will cause injury. You don't want to round your lower back while dead lifting, but adding a bit of swing to your bicep curls will not.

The idea is that you are increasing your chance of injury because you've hit short term hypotrophy of the CNS/muscle.

"To failure" is a relative term. Someone who has lifting for a very long time knows their body very well. "To failure" some days might mean they don't even finish their warmup.

The reason I started this whole conversation was in response to the quote that failure is “until you can’t maintain perfect form”, which implies it's not a relative term.