I have noticed that AA (or AAA in that case) rechargeable batteries are always of nominal 1.2V while non-rechargeable have nominal voltage of 1.5V. This works just fine in some cases, e.g. when the voltage requirement refers to just one battery and to a not really demanding load such as a tungsten lamp. In the latter case only the lumens would be affected and since this amount of voltage would normally be used as an indication lamp no harm is made.
However, in the case where more demanding loads exist, e.g. when added 3 or more batteries for an electronic device then this might just lead to stop functioning. 3*1.5 gives nominal 4.5V while 3*1.2V gives 3.6V so if the threshold is at 4V then even really fully charged batteries are inadequate to use.
I know that the nominal voltage is just an indication and a typical battery has a declining voltage, e.g. for 1.5V this means 1.6 or 1.65V fully charged, but the question is still valid.