When does idempotency become absolutely essential, not just a nice perk?

i've been wrestling with the concept of idempotency lately, especially in the context of API design and background job processing. we all know it's good to have, preventing duplicate operations when a request might be sent more than once. but when does it cross the line from a convenience to a fundamental requirement? for instance, in payment processing, it feels absolutely critical. but what about less sensitive operations? what are your team's guidelines for deciding when to invest in building fully idempotent systems?