Glancing over the patent, I don't think Hall effect sensors are used here. Note especially the use of a fluid, and the presence of variable resistors (parts that can wear out in current-gen controllers) for each axis.

Instead, this looks like an analog stick force-feedback mechanism that could also be used for automatic re-centering:

Accordingly, in the first example, control of current to be applied to the MRF is performed in the way as described below, thus achieving both presentation of a feeling using the MRF and an initial position restoration operation.

This wouldn't keep the potentiometers from wearing out, but with the right software, I imagine it could automatically adjust the sticks to compensate for mild drift. (I don't know if this would work any better than plain old calibration; it's definitely more complicated.) Also, games could dynamically adjust stick resistance, like the DualSense can adjust trigger resistance, for interactivity/immersion.

I wonder how much this would affect battery life, how long the fluid mechanism would last with normal wear and tear, and how environmentally toxic it will be when it eventually becomes e-waste.

The PDF linked in the article seems to be a scanned image, so control+F doesn't work, but the text is searchable here: https://patents.justia.com/patent/20230280850