Okay, but forgive my rather poor grasp of physics, but surely the point of entry is the key place where air inputted has an effect on a tyre's inflation, and if p = f / a, and a is constant for a given valve type, then p can only be increased by increasing f?
You said that a fatter pump would give lower pressure but shift a larger volume, but surely that volume is throttled by the valve area so that the equation above is the same as it would be for a skinny pump? As there is no v for volume in the equation, nor a velocity variable for the shifting of it.
The proof of the pudding is in the eating.
I have a stubby Lezyne hand pump and a Blackburn Airstick of the same length.
They perform as I have outlined, the Lezyne will not put much more than about 60 or 70 psi in a road tyre, but the Airstick will.
But try to pump an MTB tyre with the Airtstick, you will be there for ages, and you won't get 50psi.
Still don't believe me?
Take a look at the size of the air chambers on pumps designed for front forks/MTB shocks.
Again, very narrow because 100+ psi is required.
As with any product, the design of a hand pump is a compromise.
High volume/low pressure against low volume/high pressure, with most designs falling somewhere in between.
Even a track pump with it's wider diameter and longer chamber is more geared towards pressure.
It takes a fair time using one to inflate a 29er MTB tyre from flat.