I think there is a doc on HP somewhere on 16 bit file printing, what it does, how, etc.
To simplify: you can send a file to print via any driver and you can enable this in the PS printer via the web interface. I can imagine HP have it as an option as you wouldn't want everyone sending 16 bit files for no reason as it takes up more room and data flow. The driver or PS interpreter will down sample to 8 bit though so there is no advantage I can think of .
The APS not saving profiles is a bug that has not been addressed, who knows why it's been that way for a long time. The APS profiles are indeed 16 bit LUT . I can save all but the profiles made with the Tc9.18 charts in APS. Color Center profiles do save to the printer no problem.