Not only voltage level, but voltage stability issues come into place - lots of aids use potential splitting to invert/oscillate the supply voltage several thousand times a second and then effectively double the voltage by moving the zero volts to the minus peak. This requires a battery with a stable output, and makes the difference between the difference between an average battery working at 1.1/1.2 Volts vs. the new Rayovacs working at 1.45 Volts potentially have a 0.7V difference in potential.
0.7 Volts more is huge within a hearing aid - even if you just consider dealing with the internal resistance of the components - before you start to consider the potential for extra processor cycles etc.
So yes - squeezing the extra juice is very important.
As an aside I’ve never understood why there’s no application for a twin 312 capsule slightly larger than a #13 - but not much cause it would only need one skin.