Burn-in is a misnomer.

OLEDs don't burn their image into anything. CRTs used to burn in right onto the screen making it impossible to fix without physically changing the "glass" (really the phosphor screen).

What happens is the OLED burns out unevenly, causing some areas to be weaker than others. That clearly shows when you try to show all the colors (white) because some areas can no longer get as bright as their neighboring areas. It is reminiscent of CRT burn-in. LCDs just have one big backlight (or multiple if they have zones) so unevenness from burnout in LCDs is rarely seen, though still a thing.

So, OLED manufacturers do things to avoid areas from burning out from staying on for too long like pixel shifting, reducing refresh rate, or dimming areas that don't change for a long time (like logos).

There is a secondary issue that looks like burn-in which is the panel's ability to detect how long a pixel has been lit. If it can't detect properly, then it will not give an even image. This is corrected every once in a while with "compensation cycles" but some panels are notorious for not doing them (Samsung), but once you do, it removes most commonly seen "burn-in".

You'd have to really, really leave the same image on your screen for months for it to have any noticeable in real world usage, at least with modern OLED TVs. You would normally worry more about the panel dimming too much over a long period of time, but I don't believe lifetime is any worse than standard LCD.

TL;DR: Watch RTings explain it

Most people replace their phones before it becomes an issue. Phones are often used for small amounts of time as people pick them up to reply to a message, browse the web for a bit or watch a video. Monitors are on for long durations and have more stationary UI elements, so they will suffer from burn-in much sooner.

Burn-in isn't a light being emitted when off, it's a light being dimmer when on.

An LED works by passing current between two different semiconductors. When an electron jumps over the "gap" between those two semiconductors, it releases a photon of a particular color (determined by the size of the gap). But over time, as an LED is used, the gap can be damaged (by heat, by vibration, etc); when this happens, fewer electrons can jump the gap and thus fewer electrons produce photons. Or the properties of the gap are changed so that they emit a slightly different wavelength photon. So if you leave a particular set of pixels on, producing light, for an extended time, those LEDs will degrade more than the rest of the screen, leading that area to be discolored or dimmer. This is burn-in.

Most of the time, that's fine, because the LEDs on your screen experience wear in a more-or-less uniform pattern. Your phone is somewhat less susceptible to this, since (1) you tend to have your phone screen off most of the time, (2) there aren't as many persistent HUD elements even when it's on, as every app has its own configuration of controls and UI elements, and (3) you tend to replace a phone more often than a monitor. When you replace your phone, it's probably more-or-less evenly dimmer overall than it was when you bought it, but since you don't have anything to compare it to, you won't know; with burn-in, though, that comparison is right next to the burned-in pixels.

By contrast, a computer monitor will typically be on for 8+ hours at a time, and persistent display elements are a part of every major operating system. If you're not using the LEDs in a panel more-or-less evenly, you'll end up with a persistent image.

First of all, LED is not the same as OLED. The O stands for organic. They are more sensitive to stuff and break down over time sort of (maybe a really crappy explanation, someone with more knowledge please help), especially the blue color.

People leave a tv on a 24h news channel with a logo that never moves. Or play a game that has certain elements of the GUI that never move. That’s how it happens most often, I think.

some of us even doomscroll

That would help prevent burn in.

You'd have to have those pixels showing the same color for quite a long time, like months to years. We don't typically have our phones on that long, and with more modern OS versions, there aren't really that many things that stay on the screen anyway. What used to be burned in on phones were the navigation bar at the bottom. Gestures are default now. The icons at the top aren't actually static for long. And phone screens turn off after a few minutes. Dark mode being popular is a big help because the brightness of the screen is a factor. All OLEDs can get burn in, we just don't have as many of the things that lead to burn in as before, plus a few things here and there meant to help alleviate it.

I'm away just let the screensaver save my screen?

Yup.

In that case why would anyone ever worry about burn it

Ignorance and the fact that you mostly hear about the people with problems not the ones who just bought their monitors and carried along with their lives.

Consider that almost everyone worrying about burn in has a phone with an OLED screen, that they're not worried about. What happened with phones will happen with TVs if they ever get cheap enough to really compete with LCD.

My pixel 3a had burn in after 3 years. It's the screen gui elements that rarely change that show the burn in. On android that's the message bar at the top and the white line task switch at the bottom.

I've been hearing "OLED burn in is better now" ever since I got my Galaxy Nexus 12 years ago. But it still seems to last only 3 years.

I don't have a way to share a picture of it, but my >6 year old phone has plenty of burn-in. The keyboard, a hamburger menu, a back arrow, are all clearly visible when the screen is bright/mostly white. It's an S9+, in case that is helpful info.

mine has it from the navbar

My Ativ S with old AMOLED technology (Galaxy S3 Generation) definitely had burn in from the navigation bar at the bottom

I’ve got burn-in on my iPhone 13 Pro. Visible in very low light setting on plain background (mostly if not only from my car-navigation app).

On the other hand, my OLED TV doesn’t have any burn-in.

Just depends how much static content you’ve got

Oversimplified, lights fade over time; the ones you use more often fade faster.

The primary solution, if I understand it correctly, is jiggling. The image is altered slightly over time to change what pixels are illuminated and how so that one set is not left in the same configuration for too long. Like the ones beside each other are used in tandem and altered slightly to create the same effect. You're seeing an illusion made of quickly flashing red/green/blue/white(maybe) anyways, so it is just a more complicated type of control.

How long have you had your phone? I have seen it begin to happen around the three year mark on my Galaxy S8+ and my S20+. Slight ghosting of parts of the Wayz UI. My S23 Ultra hasn't yet, but still have a while on it.