Even in the early 90s my good rechargeable batteries (AA) only put out 1.2v when freshly charged and dropped lower than that as they ran. They also ran far shorter than duracell or similar expensive batteries.
So one the voltage may have been too low and two the usable loge might have been too short for these power hungry devices
Many 1980's electronic devices needed too much power to be run by the NiCd batteries of that era.
I failed to learn DC motors, controllers, and gear boxes in part because I lacked batteries powerful enough to drive the small motors I had. (Or maybe I was an idiot:o) Decades later, lithium 18650 cells make it easy for my students.
Nickel cadmium AA batteries (what was available in the 90s) were not great. They self-drained to flat after a month, and had "charge cycle memory," so if you discharged them a couple times to, say, 60%, that became the cell capacity. Even fully charged, they only put out 1.2v.
Nickel metal hydride, and specifically Eneloops, were a game changer, as their self-discharge was only 10%/month, and had virtually no charge cycle memory.
Not OP, but i remember having a camera that use AAs and would not support rechargeable. While it powered up, it would not take photos and instead shutdown. I think they used to be able to deliver less power, also when i put them in the gameboy the little led was a tad dimmer that non rechargeable one even when fully charged
Most of the old rechargeable aa or aaa batteries were NiCd, which would be 1.2V vs the 1.5 you get from alkaline. I believe the voltage drops off more slowly than alkaline, but since the starting voltage is lower some devices just can't handle it.
We had a set of cb radios when I was a kid, they had 12 aa battery spaces but two "blanks" installed. You used the blanks and 10 batteries for alkaline, but removed the blanks and installed 12 if using rechargeable to bring the voltage to an acceptable level.
I had a radio that could handle rechargeable vs non - it included a dummy AA battery that you used when using non-rechargeable batteries, so you'd use (IIRC) 7 rechargeables + 1 dummy or 8 rechargeables.