1.2V is only nominal voltage. 1.2V was a round number close enough to the typical voltage of those three chemistries and thus became the voltage on the label. However, every battery chemistry has different characteristics including voltage across a discharge cycle and open-circuit voltage.
Well designed electronics powered by AAA/AA/C/D cells should be designed to work down to well under 1.0 Volts, ideally down to about 0.8V to extract the most energy form the cell - any cell chemistry type. When this is the case, it doesn’t matter that NiCad & NiMH rechargeable cells have that lower terminal voltage, they’ll still deliver all their energy.
Back in the old days, though, when a lot of electronics gadgets weren’t designed to operate to < 1.0 V, the gadget fitted with NiCad rechargeable batteries would malfunction &/or shut off prematurely, and gadget manufacturers would warn customers not to use them, and to use non-rechargeable carbon/alkaline cells
Important Note! When charging batteries you must make sure that the charger voltage is less than or equal to the battery voltage. For the best battery performance/life you should have them matched