Smoke point and toxicity
All we can tell you that is provably true is that heating any oil or fat past its smoke point causes rapid oxidation and more-or-less mimics the effect of rancidity.

You should do your own research on sites like Google Scholar or just ask your family doctor or dietitian if you want opinions on whether or not this leads to longer-term health complications. There's certainly plausible evidence in favour of the claim, but the jury is very much still out on most of it, and we are all the time discovering new health risks and/or refuting previously-hypothesized ones.

Meantime, think about whether you really want to be cooking with burnt, rancid oil, and consider preparing your omelettes at lower temperatures and/or not wasting your expensive EVOO on high-heat cooking.

Personally, I can't remember the last time I used anything other than butter or bacon fat for an omelette, and I've never gotten either of them to smoke in my pan, despite unclarified butter having a lower smoke point than EVOO. Not sure why you think you need the pan so hot.