This is the real solution to PS5/PS4/Switch Joysticks drift. But it’s expensive
One of the most common pain points of all console gaming is analog stick drift. I don’t think a single console is immune to the problem in the current gen, although some of them certainly seem to be see it more often in my household (*cough*, Switch JoyCons are ***, *cough*).
Specialized site iFixIt had a detailed and fascinating article on why the problem happens (the potentiometers used in the Joysticks start wearing out after 400hrs of gameplay, or, in other words, less than a year of playing 2h daily), why “fixes” you can find online are at best going to mitigate the issue only for a short while (the only way to fix an old potentiometer is to replace the potentiometer itself, so other techniques, including software recalibration are at best temporary workarounds). Their conclusion: analog drift happens because gaming companies put cheap components into their controllers, in the name of profit.
They mention that solutions exist. The N64 for example had optical sensors to read the position of the joystick. The Stick itself was not perfect and susceptible to wear and tear, but the sensors were great.
Another “simple” solution would be to still use the potentiometers, but make them easier to replace, without soldering skills. The upcoming DualSense Edge will be providing some replaceable analog sticks, which in itself might make the controller worth its cost.
There’s however one controller that had the reputation of never drifting: the Dreamcast controller. And for good reason. The Dreamcast controller used magnets instead of potentiometers, relying on the Hall effect for its analog stick technology. The magnets have a very long lifespan, and can even be replaced if they ever wear down.
The reason these are not implemented in all recent consoles is most likely cost. Hall Effect-based joysticks involve some licensing fees for patented technology, that Microsoft/Sony/Nintendo are possibly not willing to pay.
Kits exist to replace some consoles’ sticks with Hall Effect equivalent, at a cost (for example the gulikit replacement for Switch Joycons, which effectively fixes drift for good, for about $30). But I wasn’t able to find any equivalent commercial product for the PS4 or PS5. (Let me know in the comments if I missed something!)
Hardware tinkerer Marius Heier has a video showing a DIY Hall Effect Stick for the PS4 Dualshock. As you will see he is still in the research phase, with a proof of concept showing that it is possible to implement, but this needs to be miniaturized to fit inside a PS4 controller. The impact on battery life as well as the final cost are also still unknown.