I was taught to make omlettes with a hot pan and cold (room temp) oil. My wife thinks that I'm giving our family cancer. I heat the pan quite hot, hot enough to smoke the olive oil that I add. The eggs follow the oil after one to two seconds, just enough time for the oil to spread across the pan. The oil stops smoking as soon as the eggs are in, and the omlette is finished within a minute. I have tried cooking at lower temperatures, but the oil is never quite hot enough and I usually get scrambled eggs rather than an omlette. Does anyone else cook an omlette this way? Is it dangerous?
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.
The health concern is a moot point, really. Why are you using olive oil if you're heating it past the smoke point? At best, that means it's lost its flavor, and if there's enough of it to actually taste, it'll taste burned. So you might as well just use a different kind of oil with a higher smoke point - whatever suits you healthwise, presumably something neutrally-flavored (e.g. canola, soybean, grapeseed).