Run a servo Nimh battery vs Alcaline batteries?
Some of your numbers are a bit off.

A NiMH battery on average has a median voltage of 1.2V, but will happily charge to 1.4V or more and should be considered empty at about 1V.

An Alkaline Battery, on average (many different brands and build qualities) has a median voltage of 1.5V (which incidently does lead to the 6V you mention for 1.4V?), but can be 1.6V fresh from the pack and should be considered empty at 0.8V.

Now, alkaline's have the awesome advantage that you don't have to care about empty, because you can't charge them, so nobody in the world cares if you discharge them to 0.3V.

They have the equally awesome disadvantage of a higher internal resistance compared to NiMH batteries. The internal resistance will limit the peak current your servo can draw, or else your uC will reboot because the voltage drops too much.

Traditionally Servo driven RC applications have used NiCd and NiMH for as long as I can remember. Always consider the original source of whatever you are using, it will help you weigh the options.

Because what is 4.8V, the most traditional RC voltage? It is exactly 4 times the median NiMH voltage. That's not a coincidence.

As such I fully expect your servo to still work at 3VDC, as any old-timey servo would as well, to allow for fully using up most of the energy in whatever battery you use. The 6V allowed maximum, then, is just to allow you to also use Alkaline batteries (since because of their total internal resistance, even if they are 1.6V out of the pack, once in the device they will drop to 1.4V very quickly).

So, for highest torque and lowest losses you should use NiMH, but if you then want to use NiMH for as long as possible, you have to make sure something in your system checks the main voltage stays above 4V and warns you or shuts down if it drops below that. Because discharging a NiMH to 0.5V will severely limit the number of times you can charge it.