which is the same logic as a screen if it gets THAT bad. that's not any real reason to complain about Oleds when the battery in it will die out sooner.
I have LCD displays that are old enough to vote with absolutely zero burn in sitting in my house right now, and a 1 year old OLED that has noticeable burn in, with several friends who also have ~1 year old OLED screens (including phones, monitors, etc) that have extreme burn in.
Anyone who tells you that its an outdated idea is doing free marketing.
What people describe as "OLED burn-in" isn't comparable at all to what you say "LCD burn-in" is (which doesn't really exist in a permanent way). LCDs are way more durable than even modern OLEDs, it's not even comparable to be honest.
That being said, it's improved over the early days as you said and I doubt the average Steam Deck OLED will have problems over its normal lifespan. I still wouldn't recommend OLED for heavy office use though, as you'll be able to see degradation within months of first use.
Ya, burn in isn't as big an issue now. For TVs what's more likely is if you only watch movies with bars on the top/bottom due to aspect ratios that you might not use up the OLEDs there and they start wearing out at a different speed than the content. Then you start seeing bars watching full screen content.
But it's not actual burn in, you would just need to play something special that hits those areas and not the center to even it out.