The calculations are somewhat arbitrary and very subjective. For people that are diving to 130 feet, MAYBE a 30 or 40 cu-ft bottle is needed, but the fact remains that most sport diving is done at a depth considerably less than that, probably less than 100 feet.
The problem, as mentioned already, with one of these big heavy pony bottles, is that people just are not going to use them. A 40 cu-ft bottle is absolutely ridiculous, say for a female recreational diver who is small and relatively weak and will be dealing with rough water exits, climbing a ladder etc for a 50 or 90 ft dive. A bottle that big takes a lot of the fun out of the dive for many people, and they just won't take it with them.
I would rather see more people take small pony bottles on all dives (say over 50-60 ft) rather than very few divers take ridiculously big bottles.
If we adjust some of the assumptions, we can justify a much smaller bottle...
Don't assume that the diver is going to totally freak out on the bottom, you just gotta stick the reg in your mouth and go up. In other words, why assume it takes 60 seconds to leave the bottom?
Don't assume the breathing rate is going to go super high, I would be comfortable in assuming a SAC of 1,0 ft^3/min.
Don't assume that the ascent rate will be 30 feet per minutes for the start of the ascent, in reality if people are stressed they will probably go FASTER. In the very unlikely event of a total scuba failure, I am willing to revert to the "old" ascent rate of 60 fpm (at least for the first 30 or 50 feet).
Don't assume that the diver will do a safety stop (again in the extremely unlikely event of a total scuba failure).
The reality of the matter is that scuba units rarely fail completely. Generally the diver that needs redundancy has been stupid and inattentive and has breathed the tank too low (or it is getting hard to breath). If this is the case, then the diver can switch over to the pony at the first indication of a problem, begin the ascent and then when they are making headway, getting their breathing under control and are reaching depths that they are more comfortable with (say 50 or 30 feet), they can decide to switch back to the main tank and "milk" some air out of it. If they can do this, they will be saving the pony gas and can contemplate the practicality of the performance of a safety stop at 20 feet or so. You can gently sip a large tank for quite some time at 20 or 30 feet, even if it was close to "empty" on the bottom. This might also be practical if a tank is free-flowing... it can still be used for part of the ascent... maybe....
A few years ago, I ran out of air, while solo in 120 or 130 feet and I was completely out of breath when it occurred. My sac rate was probably 1.5 when the tank got hard to breath. I only had a 6 cu-ft pony... I made it to the surface, used a little of the main tank and did do a safety stop, but you can be damn sure I didn't screw around on the bottom, or ascend at 30 feet per minute for the first 60 feet.