Very interesting set of questions. My comments:
Lately I've seen more and more divers, usually newer divers, request for larger and larger tanks. AL80s are the 'standard' by and large. Requests come in for 100s and now 120s and 130s.
I don't think it is at all unheard of for new(er) divers, who recognize that their air consumption is relatively high - frequently higher than their more experienced dive buddies - to attempt to address their concerns about either short bottom times or potentially rurning out of air, by requesting a larger cylinder. I did that, years ago, and purchased a 120 right after certification, for those very reasons. It is a new(er) diver phenomenon. There are mutliple SB threads on the subject, often started by newer divers lamenting their high air usage and asking for advice. And, the fairly common set of responses usually includes, 'It will get better over time, as you relax and become more comfortable', along with comments about optimizing weighting, buoyancy control, trim, finning style, exposure protection, gear configuration (streamlining), etc., etc.
Why you are seeing more of this recently is possibly a reflection of a) you becoming more aware of it, b) the experience profile of divers that you are encountering has shifted - to a lower level of prior experience, c) new(er) divers being more aware that larger (than 80cf) cylinders are available, d) dive operations actually beginning to use / have available larger cylinders. I don't know that human physiology has changed, or that more divers are finishing OW with poorer skills (although I feel confident that some will chime in that such is obviously the case). Of course, in the absence of any discerniblle reason, I would conclude that this is the result of global warming - after all, virtually everything else is.
Most commonly seen underwater for those who request or insist on larger tanks: averaging 15 breathing cycles a minute with outliers at 25.
Normal adult resting respiratory rate: 12 - 20 / min. The 'outliers' are that, but tachypnea among anxious people underwater is fairly common.
Should divers learn to relax while underwater and breathe slowly or be encouraged/allowed to continue (by supplying larger and larger tanks) to come close to hyper-ventilation and 'still have enough air left?'
I don't consider this to be an 'either / or' situation. Most definitely, divers should be reassured that this is not uncommon in new(er) divers and will improve with time, more experience, and continued skill development, and that they should actively work to breathe slowly and deeply - in fact to practice that technique on land as well as in the water. I don't have a particular problem with new(er) divers using a larger cylinder as long as that is not the only solution employed, and they simply continue to breathe, swim, fin, and rig their gear the same way, without any attempt at modification. It is something that I try to address during OW training - beginning in CW - but I also tell students that relatively high gas consumption is to be expected at first.
For the more educated on the topic of DCS (not me) will breathing that much more gas at depth, say 50% more by comparing 80s to 120s will there be an adverse impact on the diver using the larger tank? Easier chance of DCS or same? Two assumptions. First being same size/height/weight approximately and second differing stats.
Theoretically, the nitrogen loading for a diver consuming 120 cf of air, at a given depth over a given bottom time, should be greater than that of a diver consuming only 80 cf of air under the same conditions. Given that a) most recreational dive tables and computer algorithms are rather conservative to begin with, and b) the incidence of DCS among recreational divers is rather low to begin with, I would not personally be concerned about a likelihood of harm. But, maybe I am just oblivious.
