I tried to conceive of a situation where the flat discharge rate would not be preferable and came up empty.
Here's a quickie: handheld radios generally have two power settings, "low" and "high". Low cuts down the transmit power to a specific amount, maybe 1 watt. High generally just belts out as much power as possible, shunting the batteries straight to the power amplifier in the radio.
Current is supplied "on demand" by the load (transmitter), drawn from the supply (battery), as long as the supply can support the demand being made by the load. This is true of any electronic device. The supply dictates the voltage, the load (by its resistance) determines the current. (voltage = current x resistance, power = current x voltage = voltage^2 / resistance)
So I can increase transmit power by lowering resistance in the load (switching transmit power to hi, which lowers load resistance, which raises current so long as voltage remains constant), or by raising the voltage
What all this means is that if voltage drops, my transmit power is also going to drop, and there's nothing I can do to compensate. (since my load is already at maximum draw, by presenting its lowest possible resistance) So while my battery is discharging with use, if my voltage drops significantly during discharge, my radio will rapidly lose transmit range. Once I am out of range of the other radio, that's it, the radio is useless for communications. And with (power = voltage^2 / resistance), power drops with the SQUARE of the voltage drop, so losing voltage is a
big problem when power is important. And it gets worse. With radio, you need to quadruple your power to double your range... so range is more closely related to voltage^3 !
I would much rather the batteries maintain their higher voltage as long as possible, and "die suddenly", with the voltage jumping off a cliff at the end. Any power remaining in the battery after the voltage falls below a certain point may be totally useless. The only problem there is you have to pay more attention to the remaining capacity, because you can't just look at the voltage to determine how much charge remains.