I'll play devils advocate for discussion sake (although I think both systems are valid) and will leave some of the more inflamitory statements aside.
You have two tanks where either one can become worse than useless at any time
How can a single tank become any more "worse than useless" than a double. If one thinks along DIR/Hog lines a doubles set up has more failure points than a single tank set up.
And assuming the pony has gas in it, is turned on and you did not breathe it down by accident
and assuming the doubles have gas in, both posts are turned on etc... You are confusing diving skills with equipment and assuming that someone who uses a pony will have less skills than someone who uses doubles. In fact, someone with good skills will be just as safe while someone with poor skills is worse off with doubles in an true emergency as identifying and isolating valves you can't see is far more complex under stress than working a pony you can see (but I won't defend poor skills to far down the path).
and is in no way a part of your gas plan
My pony is part of my gas plan (Unless you mean part of the gas one plans to breath on a routine dive which I do agree with). It is part of my emergency air source supply, along with reserve back gas.
In general the doubles are sounder as they have just as much "redundancy" but you can isolate them and save your gas if you have a problem.
Depends what you isolate doesn't it? If you isolate a second stage, yes, you have access to both tanks but if you shut down a stem valve you've lost that whole side in which case they are just as redundant, not more sound.
Here's a real problem, not of doubles themselves, but of their common usage, that I have seen. I alluded to it in my most recent previous post; multiple dives on doubles.
If you can follow my reasoning:
A doubles diver entering the water on the second dive (assuming they used half their back gas on the first dive) having as much back gas as I do on a single tank but I also have a 30cu.ft. pony.
When the sh-t hits it on the last part of the second dive the doubles diver has little back gas to work with (this is what I meant by where's the redundant air source). They become buddy dependant for meaningful redundant gas
or have to be diving a very conservative profile. The question is whether buddy dependance is more sound than self sufficiency? A safe diver would, of course, dive the conservative gas plan but I don't always see that in practice. I see doubles divers diving the same profiles as single/pony divers.
Here's another way to look at it:
..........................Doubles diver...................Single + pony diver
First dive..............80 + 80 (160)cu.ft. ..........80 + 30 (110)cu.ft.
Second dive..........40 + 40 (80)cu.ft. ............80 + 30 (110)cu.ft.
This has nothing to do with whether one is a good buddy, team player etc... or not. just with the actual state one finds themselves in. Each person has to decide whether they will ever experience buddy seperation at a critical time and what position they want to find themselves in when/if it happens. On the first dive both systems provide good coverage but on the second dive the doubles diver has to plan a shorter dive, not lose their buddy or push the safety envelope.
I want to be the fly on the wall on a boat charter when the doubles diver tells the single/pony diver they want to dive to the rule of thirds instead of halves.
It would be the correct thing to do but I wonder if ego's would interfere with common sense.
PS. A soloist on the second dive with doubles would be at even more risk IMO.