Wayland does not support screen savers: it does not have any provision that allows screen savers to even exist in any meaningful way. If you value screen savers, that’s kind of a problem.
Adding screen savers to Wayland is not simply a matter of “port the XScreenSaver daemon”, because under the Wayland model, screen blanking and locking should not be a third-party user-space app; much of the logic must be embedded into the display manager itself. This is a good thing! It is a better model than what we have under X11.
But that means that accomplishing that task means not just writing code, but engaging with whatever passes for a standards body or design committee in the Wayland world, and that is… how shall I put this… not something that I personally feel highly motivated to do.
That’s what the display makers claim, in order to avoid too many customer complaints. In reality you’re still likely to get burn-in within a few years of monitor use, and when you ask for warranty support you’ll get denied claiming “you used the display wrong”.
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People don’t tend to keep phones for more than few years. On the other hand, I have LCD computer monitors that I still use over a decade later.
What really kills OLED displays is persistent static elements. These are common for desktop usage: persistent taskbar/dock, desktop wallpaper, window buttons, tiling, GUI elements and HUDs in gaming. All of these things significantly increase the chance of getting burn-in within a few years.
OLED fanatics suggest it’s all user fault, that people should just use a solid black background for their desktop wallpaper (ugly), have a auto-hiding taskbar (inconvenient) and limit time spent on programs/games (really). Basically rather than using the computer the way you want, you have to carefully handle it like an egg. An expensive egg at that, since OLED displays are still ridiculously overpriced (often costing more than equivalent TVs).