A related question: Why do all the 744's (at least the ones I've flown) have a #4 aux pump while only some have the #1 aux pump? Obviously the aux pumps are there to supplement the relatively limited bleed capabilities of the APU's bleed air and prevent it from having to supply the Air Driven #1 and #4 pumps during engine start. Is the #1 aux pump just a nice luxury that some operators elected to pay for in their orders from Boeing or is there a reason why some planes need it (pax, BCF) and others don't (freighter)?
The #4 aux pump provides brake pressure without needing a running engine or APU. Handy for all sorts of reasons. The optional #1 aux pump allows for body gear steering in the same configuration. In plain English, an airplane with both #1 and #4 aux pumps installed can be towed with just a GPU plugged in.
It does not have to do with bleed demands on the APU (MEX excepted!). As noted, not all airplanes have the #1 aux installed and the MEL allows the #4 to be inop; the end result then being that the push back and engine starts are done with the #1 and #4 demand pumps working via the APU bleed.