Your "logic" is impeccable.
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Been using the same 2 pairs of Energizer rechargable 9 volt batteries in my phono preamps for 3+ years (use one pair while slow charging the other pair).
A quad of rechargable AA's last a year in my digital camera (after camera duty they are still usable in remote controls and flashlights for another year, or so).
I don't have the energy to purchase and throw away 100's a batteries each year.