There are different sorts of BEC circuits: linear vs switching
A linear regulator does "drop" the difference between the battery and the BEC output across the regulator. Linear regulators are inefficient because the power dissipated in the regulator is then the current load times the dropped voltage.
Switching regulators chop the input voltage into a pulse train and take power as needed to maintain the load current at the programmed voltage setpoint.
The end result is that switching or SBEC's would not get as hot as a linear BEC. I think most newer BECs are the switching type.
Servos are not linear resistive loads so Ohm's law does not apply. The current draw depends mostly on the mechanical load.
All that being said, I would not run a 6V rated servo at 7.4 volts. It is really not clear to us consumers what limits the allowed input voltage. I have read some guys say that 6V rated servos are specified at the 5S NiMh "nominal voltage of 1.2 volts per cell. But when fully charged, 5S NiMh is more like 7.2 volts (a least at the start of a run). I have personally run some 6V type servos with 2S LiFe which s 7.2 when fully charged but is really more like 6.5 volts within a few seconds of use. Never had a problem with those.
I just always try to buy HV rated servos these days so I can use them anywhere from 6V to 8.4. If it is a 6V rated servo, keep it at 6V (or 2S LiFe at the most). You might get away with it at 7.4 volts but there is no telling ahead of of time.
As far as the Savox causing brown-outs. These cars only have one freakin servo. Maybe two for a Nitro. Its a sad BEC that can't drive one servo. In helicopters we have four. If that particular servo is a big current hog, it is probably only for short intervals. You could try getting one of the those electrolytic capacitors like this
https://hobbyking.com/en_us/turnigy-...protector.html
It will source extra current for shsort times and reduce the transient load on the BEC. You can also run a small 4S NiMh buffer pack. The 6V BEC will keep it charged without over charging.