Is a decoupling capacitor theoretically required across the supply pins of a Hall sensor?
There are several reasons to use the 100 nF capacitor: -


The data sheet recommends it
The internal chip current changes by 2 mA when it switches
The external load (attached to the open collector output) might switch an extra 20 mA
The supply voltage may not be a perfect voltage source i.e. it might have ESR and ESL components that would cause a ripple voltage on the supply when the device switches
The cable supplying power to the chip might be long and have more ESR and ESL
Switching times are around 100 ns i.e. it switches at a fairly high speed.


I don't see any good competant reason NOT to use it.


  how would the current source of the Hall element (which apparently is
  a voltage regulator across a constant resistance) be less stable
  without cap, given that there is nearly no load, and that the power
  supply rejection is not so important (since this is a digital sensor)?


The first part is impossible to say without detailed knowledge of the device. There is an internal load and that load changes by 2 mA each time the device switches and, it switches in about 100 ns. There is a graph in the DS that shows this. Power supply rejection being unimportant is not a healthy place to start making a counter argument.