There shouldn't be a problem, I agree. The only 'problem' I had when designing the EEPROM programmer was making it all work with the limited number of pins on the Atari's joystick ports.
The idea behind everything was to make it as simple as possible by avoiding having to add any control lines for the programming voltage. Initially, I had hoped to use something like a charge pump which would increase the voltage from the +5v on the joystick ports. Got a couple somewhere, I think. The DC to DC converters I was thinking of are the step-up converters, rather than the step-down regulators.
Another possibility which I've yet to look at is using an I/O expander chip. I've got some MAXIM 7300 chips which are quite impressive and give you 20 I/O pins. With this I'd only need to use two pins on a joystick port for both input and output (well, one pin to be exact - the other would be used as a clock signal), thereby leaving me with 6 other pins for additional control logic if need be (or add 3 more 7300 chips for one helluva hardware controller with 80 I/O pins!!

).
The only problem I can think of with this approach (i.e. getting the Atari to supply all the voltages to the programmer) of trying to avoid having to use an external power supply is that, whichever method I choose, there probably wouldn't be enough supply current to the EPROM - so I'd probably need an external PSU anyway.