In devices that could potentially pull a high drain and whose circuits are so designed to rely on Alkalines to restrict the draw may be damaged by rechargeables or cause those rechargeable batteries to overheat and catch fire.
However, some my low drain chess computers say to not use rechargeables and I suspect the manufacturer could not be bothered putting in the extra bit of circuitry to convert the current into the correct voltage while also guarding against a too higher power draw.
As a point of interest, back in my CB says I had a handheld unit that came with a rechargeable battery cradle for the standard battery port. When using rechargeables, it required fewer cells and attained a longer range - demonstrating the ability of rechargeables to throughput more power on demand.
Perhaps a dumb question but the DGT PI according to the producer DGT in Holland should not be used with " rechargeable batteries ". Printed in the User Manual page
In this times such a company does not care a bit about being ¿ a bit ecofriendly ?
I can only imagine that the slightly lower running voltage of rechargeable batteries is not liked by the Raspberry PI inside ¿?
And BTW the Raspberry PI is a powerful computer. Why did they not add a simple battery NiMH charger for two rechargeable batteries ?

Maybe this post is ridiculous but I think we are aware of what we are doing to the Planet Earth ...
Maybe here is the answer ...
https://cleantechnica.com/2017/07/12/netherlands-one-least-sustainable-eu-countries-dutch-get-green-image/
https://auclimate.wordpress.com/2020/04/15/the-netherlands-sustainable-image-how-much-is-true/