One issue from using a switcher to step up battery voltage is that even with perfect conversion efficiency the current draw gets multiplied proportionately. So whatever mic current draw , will get multiplied between 5x and 6x from the 9V battery, even more from 1.5v cells. 9V cells are a couple hundred mA hours so do your own math for life expectancy. THe AA cells have more mAhrs, but less V so it pretty much cancels out. With batteries it's pretty much like capacitors so size or volume determines current output across similar battery technology. A switcher will have some overhead loss related to switching device on resistance, so higher battery voltage will run at lower current "and" be less affected by the switch forward voltage loss.
Note: some phantom powered mics will operate Ok with less than 48V. As I recall Peavey used to sell an accessory phantom supply that provided only 9V. many install products use +15v phantom. While I do not expect 9V to be enough for "all" mics.
If you have a specific mic in mind, and apparently you do, perhaps consider some bench testing with a variable PS to determine how much voltage you really need. If you can get away with stacking two or three 9V cells, you will get pretty good life, with a lot less complexity. If you really need the full 48V use a switcher.
Back in the bad old days when they still made portable tube radios, I recall seeing 24V (?) or so batteries. These days high voltage batteries are not as common.