Having done over 1300 free fall skydives I think I may be qualified to comment on this topic. I used to have 3 different altitude sensors all based on air pressure. A wrist mounted altimeter with an analogue readout. An audible altimeter which was set to give an continuous bleep when I reached a set altitude and rate of descent. An CYPRES altimeter to open my reserve parachute if I was not under canopy by 1,500 ft. All three altimeters were zeroed each time I put on the parachute so that they measured altitude relative to the drop zone altitude.
Only the wrist mount altimeter was mandated; the other 2 were optional (this may have changed now). The wrist mount display had three bands. White for above 3000ft, yellow for between 2000 and 3000ft and red for below 2000 ft. Being analogue and colour coded made it easy to get the important information without having to spend too much time looking at the altimeter.
A typical free fall starts at about 12,000ft and one gets to terminal velocity of about 120 mph after about 15 seconds. The total free fall time is about 60 seconds. The only information one has time to deal with is one's altitude and I would be very very uncomfortable with an altimeter display that was cluttered by superfluous information. In the UK, one has to deploy one's main canopy so as to be under canopy by 2,000 ft. This then allows one to revert to plan B (using one's reserve) if the main canopy fails to deploy properly.
I can see little advantage to having more information than altitude available during free fall.