No it doesn't. Again. No. It. Does. Not. That is flat out wrong. Correlation does not equal causation. If you want to try to prove that there being mentor achievements causes toxic mentors, you're gonna need to show some evidence. Sorry, your anecdotal evidence does not count. You are the one making the claim, you have to provide the evidence for it.
For a lot of people complaining saying mentor system should be abolished, they think mentors who leave extreme trials without a word or who let sprouts know that if they want to clear an EX trial, it's a lot easier and far faster to put up a party finder and they can do it unsynced is toxic? Perfectly valid and viable suggestion since most just want to clear and not do it synced specifically. I've seen as presented as evidence over and over and over again in these types of threads. Leaving a duty and taking a 30 minute penalty because you know the fight is just gonna be a huge waste of time when it is synced with a random party and only an hour to clear and making no progress or getting a clear is not toxic behavior.