To me, the ideal default is PianoStaff.
1) (another example) In a 4 hands piano score this would be undesirable, because it would logically assign the pedal to *one* performer, while it can switch from performer1 to performer2. For example: it would be nonsense that bars that are executed only by performer2 are given to performer1 for the pedal only.
2) The Staff context would be common for *all* the instruments that use a pedal, considering that *not all* have necessarily a pianostaff (for example: a vibraphone)
3) I never saw in my life a pedal bracket fragment in upper staff and another fragment in the lower one, but it can happen that a *new* pedal belongs to another staff than the previous one
4) In any case, IMHO there's no reason to assign Piano_pedal_performer to Voice. This seems abstract midi, with unwanted/weird results for the user
Best would be to move the engraver as deserved. How to move engravers
is documented already...
So I can't see any need to do anything.
But IMHO this is not user friendly. Lilypond's users do use a piano template, and they should not care about these details, which are not included in the piano section of the documentation.
And not only the described unwanted behavior should not happen as default (see Timothy's observation about consistency):
before fixing the inconsistency in future releases, it should be at least documented with a workaround for avoiding it. Note that, without Timothy's addition, piano pedal bracket is correctly drawn but wrongly performed, which is highly misleading...
This is what I think.
HTH
Best
P