That being said, it is reasonable to believe that no sec-2 curve has an NSA backdoor.
Believing that it doesn't have an NSA backdoor is reasonable. However, you can't throw it around the board as a fact. We don't have evidence of it being free of backdoor. We simply know that it's open for public scrutiny years now, and that a backdoor in such an examined algorithm would be likely discovered by now. That doesn't nullify the doubt.
It’s some unique quality but in one instance, you serve as mixers and coin offerers all in one.
Cash has existed for centuries, in much larger scale, and is equally or even less traceable than Monero. Yet, no user was subjected to using its banknotes for "mixing". Everyone accepted it.
I have been thinking about this as well and I am all for never say never here. There have been examples for backdoors that went undetected for decades.
But I find one idea quite compelling to think about, do you think that publicly available artificial intelligence will come to a point where it can be asked for vulnerabilities in the most secure (or rather most pervasively used) algorithms or could it intentionally be fed an information a la garbage-in-garbage-out such that it always provides an answer pleasing the public? If AI becomes more intelligent at an exponential rate while an algorithm is a static mathematical construct, would the chance be that those developing AI would/could be the ones to know first?
What I also wonder is whether a backdoor could in any case be detected as having been introduced deliberately by someone? I am sure there are cases where it could be, but there are probably cases where someone could say it was just a mistake in the code.