You're right that if not competing there's little reason to test 1RM. The one reason might be if your lifts are quite high, you might need 1RMs to plan your progression. That sort of periodisation is beyond what I work with, though, so I don't comment on it.
What I would say is that it's not 1RMs as such that cause injury, but maximal efforts - of however many reps. The maximal effort leads to a degradation of form which leads to injury, or else the maximal effort affects some tissue which was already weakened by your previous activities, injuries or background.
I don't see how anyone can progress without consistent efforts over time. And from time to time, some of those efforts will have to be maximal. I simply don't see how you can progress without at some point going, "fuuuu...." during a rep - those reps where you know you'll complete it if you push, but the next rep would fail.
So a certain amount of risk, I think, is inevitable. All you can do is minimise it, and decide whether the risk of injury is worth the rewards - so it's good you're considering it against competition, weighing things up like that.