Second off, instantaneous sound is only a health issue when it's really loud, like a gunshot (130-140dB SPL) near the point at which the ear drum ruptures. That means that you need to be in an environment where the background noise is dangerously loud to begin with, and because of the way sound is made - this might be unlikely. Which is interesting, because early ANC did have these problems - when it was being used initially for military applications (helicopter/tank pilots iirc).

Lastly the important thing to remember is that ANC is usually part of a dual pronged approach to ear protection. Latency is a problem when you need to cancel high frequencies (where you get past about a quarter wavelength and interference can become constructive), but ANC excels at low frequencies (below about 500-1kHz it can be remarkable even). This is great because passive reduction strategies (sealing off the ear, thick padding, good fit/headband adjustment) are much more effective at high frequencies.

So TL;DR it was a problem, been fixed, and where it might happen is pretty rare for a consumer.

Also noise rarely spontaneously inverts phase at a particular frequency. That'd be weird.