I suspect that the primary reaction is simple weariness, resting your trunk muscles rather than just trying to get more breath. The next level would usually be to hunker down or even end up on all fours, right?

However, I reckon that the effect on breathing is to place your abdomen and chest in such a position that they are under the least tension, and therefore that there is least resistance to your rib cage expanding to fill your lungs with a large volume of air.

This also would minimise the muscular work that you would require to expand the rib cage, and accordingly the amount of oxygen that your breathing effort itself demands, either for inhaling or exhaling.

Certainly, standing erect and bending over backwards with your arms and shoulders raised draws air into the lungs; similar positions were the basis for early versions of artificial respiration, but your need when exhausted is not to get as large a volume of air as possible into your lungs, but how much air you can pass through them, partly to flush out CO2 and partly to collect oxygen. Having filled your lungs in that strenuous fashion, you next have to reverse the process and repeat it.

It is far more efficient to swing a passively dangling belly ad let the elasticity of your rib cage take care of the recovery stroke.

Just an opinion...

Jon