

It boils down to chemistry. The nickle-metal-hydride chemistry used in rechargeable batteries just don’t produce 1.5V (explaining why is a lot more complicated), while the alkaline chemistry in non-rechargable batteries produces slightly more volts.In the same vein, lithium-ion batteries produce around 3.6V, while lead-acid produce about 12.4V.
To answer your other question, they should be able to power most things that aren’t an analog clock (which might run slightly slow).
Not sure where you’re located, but at least in the USA it’s definitely illegal for an employer to discriminate against a medical diagnosis like that. They aren’t even allowed to ask you private medical questions during the hiring process.