4 pieces of information that are critical for every diver:
1) Depth
2) Time
3) Gas
4) NDL
Does it matter how you get that information? No. You just have to have it.
Depth can be gained from a variety of sources; computers, depth gauges, knowledge of the dive site...even from marked lines. It is not feasible to accurately estimate depth by visual, or other, indicators.
Time can be gained from several sources; computers, watches and other gauges. It's not feasible to accurately measure time over the space of a dive by counting.
Gas can be gained from either an SPG or J-valve. Knowledge of your air consumption, used to predict gas use over time isn't the same as knowledge of your actual gas status...and doesn't mitigate against certain risks, such as; gas leak, accelerated SAC etc.
NDL can be gained from a dive computer, tables, desktop/laptop software or mental calculation (i.e Ratio Deco). All are valid, providing the diver follows the correct procedures, plans the dive and follows the plan.
Other information, such as; ascent speed, no-fly time, emergency deco etc aren't critical; but they do help to further mitigate against risk and add convenience. All of this information is available to divers, without reliance on a dive computer. A computer just adds convenience and can reduce task loading.
Every agency and most experienced divers will recommend that every diver has independent access to that information. The logic behind that recommendation is that it allows each diver to mitigate against a range of foreseeable scenarios; the primary risk being that of buddy separation.
Sharing a dive computer essentially puts one diver into the role of 'trust me'... where they are completely reliant on a buddy to provide that critical dive information. It's impossible for that diver to plan or track a dive on their own. It doesn't add risk, but it does fail to mitigate against potential risks that have been proven to exist.