Wired in 4P, for example, an MC-E would get 250mA per core if you drove it with a boost driver rated at 1000mA output. The trick is if the driver can actually reach regulation when powered by two AA cells.
If the cells are AA Eneloops, then I believe a good quality boost driver can run in regulation. If the cells are AA alkalines, then the driver might run in regulation for the initial turn-on, depending on the boost driver. But subsequent turn-ons may very well not make it to regulation, once the cells are no longer fresh. Thus, instead of using a boost driver with 1000mA output and having problems reaching regulation, you might go with a driver with 750mA output instead.
It all depends on the boost regulator IC. Often these ICs have a switch current limit of around 1.5A or 2A. If the limit is 1.5A, the driver might reach regulation with Eneloops because #1, the Eneloops can hold a higher voltage under load, resulting in #2 a lower current demand from the batteries, and #3 barely making it under the 1.5A switch current limit. In contrast, AA alkalines will probably suffer greater voltage sag (especially when the cells aren't fresh anymore), requiring a higher current from the batteries to deliver the power necessary for a 1000mA driver output, and potentially exceed the 1.5A switch current limit.
If you can reach regulation and drive the 4P MC-E at 250mA per core, an M-bin MC-E could deliver over 300 emitter lumens, with a very low forward voltage, and thus a very low power consumption. For the comparable Seoul P7, I measured Vf of 3.07V at 250mA per core, or just about 3W power delivered to the LED. If your have a 90% efficient boost driver and are using NiMH cells that can hold 1.3V per cell for a few minutes under say a 1A-2A load, then
0.9*2.6V*Ibatt = 3.07W (using the Vf data from the P7 I measured)
and
Ibatt = 1.3A.
Here is the difference when underdriving a quad-core LED like the MC-E. For a typical single die emitter like a Cree XR-E or Seoul P4, you might get a forward voltage of about 3.5V at 1000mA forward current (which might give about 240 emitter lumens). With this higher forward voltage, the same calculation as above gives Ibatt = 1.5A. Thus, the lower Vf for the underdriven MC-E could make the difference between running in regulation or not.
Now if you change the driver output current to 750mA (188mA per core, or about 240 emitter lumens), then
0.9*2.6V*Ibatt = 3.0V*0.75A
and
Ibatt = 0.96A (this assumes that Vf=3.0V at 188mA per core)
Even if you use AA alkalines that might hold 2.2V, Ibatt~1.1A. So, most likely a boost driver rated to deliver 750mA output current can reach regulation with just about any type of AA cell chemistry.
My guess as to why you don't see lights like this is because buyers want and expect huge lumens from quad-core LEDs. They are not interested in underdriven MC-Es and P7s, despite IMO the clear advantages vs single-die emitters. Also, in some sense, there is probably the perception that the LED is being wasted on such a low output, even though the emitter lumens is probably 30% greater than that for a single-die LED while running probably at least 10% more efficiently. That 30%/10% gain in output/efficiency is probably just not compelling enough to a flashlight maker.