Tangentially related: one of my all-time favourite neuroscience papers by Iriki et al. [1] showed that the mouse pointer becomes part of the body schema in a real, measurable way.
Basically there are neurons whose receptive field (ie the subset of the outside world that causes the neuron to fire) is "everything a monkey can reach". Flash a light in that area, that neuron fires, flash it beyond that area, neuron stays silent.
Now if you give the monkey a rake, the neuron's receptive field immediately grows to encompass the space it can now reach with the rake too: the rake becomes part of the body schema, not part of the outside world [2].
But if the rake instead is just a stick but it controls a mouse cursor on the screen, the _area of the screen_ the monkey can interact with with the cursor becomes part of the receptive field of that neuron too. That suggests that the cursor itself becomes part of the body schema.
TL;DR don't mess with people's mouse cursors, it's like cutting their limbs off.
[1]: https://pubmed.ncbi.nlm.nih.gov/15588812/ [2]: A wild Heidegger appears and talks about Vorhandensein and Zuhandensein.
> TL;DR don't mess with people's mouse cursors, it's like cutting their limbs off.
“Don’t mess” is a very broad range that includes things like removing the mouse cursor at nine PM. Of course, no one should do that.
But a narrower conclusion “let the mouse warp at certain predictable cases” doesn’t contradict your thesis.