It's not a gargantuan frame pump (as the Brompton doesn't have a gargantuan frame) but although it would easily fit in your bag it's nice to know that it's on the bike if you forget, or decide to go out without, your bag for some reason.
When I first saw the frame fitted pump I thought that (a) it was in a good spot to collect all the road muck thrown up by the back wheel and (b) what a world of misery might occur if it fell off into the spokes, even though (c) it was very neatly and discreetly mounted. I thought the steering stem might be a better place, using conventional clips, and might even accommodate a usefully longer pump. That wouldn't affect the usefulness of the rear rack as a mobile stand, or affect the ability to strap things to it while riding. I haven't measured up or tried anything yet as the bag containing a spare pump is always on the bike at the moment, and I can anticipate any alterations affecting the fold so it needs careful thought.
Also it might be less aesthetically pleasing to have it on display, as well as being a temptation to any passing scrote who might be looking for a chance to spoil someone's day.