When I was a child my parents had a purely mechanical scale, with a dial to adjust the zero.

Yet another case of why fix what isn't broken. Only, I expect that an IC or two and an lcd to run a digital scale are cheaper at volume than some amount of mechanical clockwork, once the cost of batteries is pushed off on to the consumer.

A quick glance at Amazon seems to confirm your intuition. The cheapest mechanical scale I can find is $32 but there are lots of electronic ones for ~$15.

We used to have one like that, too, and I don’t remember it being capable of single-gram accuracy like my cheap IKEA scales are.

Since scales inherently involve putting weight on them it should be possible to use that weight to push down a plunger generating enough electricity to run for the weigh-in.

A spring would then reset it for the next time.

If there's a plunger resisting the scale going down to harvest energy, that would prevent all the force from being on the load cell, giving you incorrect readings.

Not if the plunger rests on the load cell. Then plunger just captures the work done as it is compressed, it doesn't reduce the force that passes through it (once at equilibrium.)

Couldn't you subtract the resistance of the plunger and display the adjusted value?

You can put the switch in between the plate and the force sensor.

Then all the force is on the sensor and is also a switch.

Have had a similar model for like 5 years now. No regrets yet. The small effort it takes to power it up by far outweighs all of the disadvantages of a battery.

Before that I installed a switch in the scale we had to erradicate battery drain.

I love the idea, but the non-flat top, and the display on the flat top kill it (and admittedly, most cheap kitchen scales) for me. If I can't put a big bowl on it and still see the readout it's useless to me.

I haven't used one so not going to pick one to link, but a quick search finds scales that claim to run on ambient light.

Based on a 30 year old calculator I have, I would expect them to work fine.