Term for "will consume time and almost certainly yield nothing"

"Exercise in futility" is an idiomatic term that describes that scenario.

Definition: a useless action that cannot succeed

Response to: "I'm going to have one of the developers contact Apple and ask them to add a new feature to Apple Maps."

"That would be an exercise in futility!"

You could perhaps call it a wild goose chase:-

a worthless hunt or chase; a futile pursuit.

A fool’s errand came to mind. Definition:

An attempt to do something that has no chance of success.
Billions of dollars have been spent on long-range weather forecasting, but it’s a fool’s errand.

The first phrase that came to mind for me is "time sink"

1.(informal) Something that consumes a great deal of time, usually with little benefit; a waste of time.

Almost matches your definition word for word.