In places that aren't America, it's often a legal requirement (whether by statute or by customary contractual clauses) to give a minimum notice period, and employees who resign without notice can be penalised an amount of money that may be non-trivial for many workers.
FWIW, in the UK notice periods are not worth enforcing either, you have to prove (as the employer) that you incurred extra costs because of the short notice which is tricky and usually not worth it.
Seems like a good way to incinerate your professional relationship with your outgoing manager. I guess if you would never use them for a reference anyway, that's fine, but what if you do want to use them as a reference in the future?