I never understood this in the context of when you had bad managers, your organisation never supported you etc. There weren’t any bridges to burn in the first place!
If you weren’t supported initially whilst they were meant to be managing you, why would they in the future? They’ve already shown their true colours.
I think this phrase comes out of insecurity, ie having somewhere and/or someone to fall back onto.
There is no incentive to maintain these bridges if your organisation and managers didn’t treat you well initially. In fact, I’d rather the bridges were burned.