I'm willing to fall for some credible marketing that convinces me I could spend a few hundred on a non-stick pan I could hand down to the grand kids, as with cast iron. But it doesn't seem to exist at the moment.
Given the additional soap and water, I wonder if it would be greener to scrape and scrub my eggs off of a sticky pan instead. It'd be better exercise.
Mostly though I agree with your point that it makes little sense to spend big money on an omelette pan. The coating is going to be pitted within a year or two, and that’s that. A good guide to how you should buy these things is found in the restaurant industry which does what you do now; buy them and toss them.
That also leads to the best advic I can give here... buy your pots and pans from restaurant surplus stores or closing sales! I bought half a dozen omelette pans from one of those for $35 bucks, and I just swap them out every two years.
I've spent a lifetime hearing this and not being able to achieve anything close to it on cast iron. Either it's false or a skill that's beyond me. Either way I've quit worrying about advanced semi mythic forms of cast iron seasoning and just use non-stick.
I use a very seasoned cast iron pan regularly to sear meat ... and a little piece of chainmail to scrape off the clingons.
Non-stick caught on for a reason!