It doesn't need to care whether someone else is handling it. It should just do what it needs to do according to its contract. The caller that receives the promise as a result has its own contract that may or may not involve handling the error as well (and so on up the chain).

You generally have to have an end-of-the-chain catch as a safety precaution. If you don't have one and the promise fails you may get no feedback that an error happened at all. All methods that return promises should be able to expect the caller to handle them appropriately whether they pass or fail - it's not their responsibility to try and figure out how to handle an error in the context of the wider application.