While your dictionary or thesaurus may list a pair of words as antonyms, there’s a chance they really aren’t diametric opposites. For example, the opposite of cold is hot, not warm. Before you drop a word in as an antonym, look beyond the first definition and think about precisely what you want to convey.
Something can be useless for a particular task even while it is fully operative, aka, functioning, or in working order. Useful is the best word to express the opposite of useless. Example: New batteries made the television remote operative but it was completely useless as a hairbrush.
Since worthless means of no value, its antonym is of great merit or value, not just passable or adequate. Example: The barren tree was worthless as shelter from the rain but the abandoned shed provided adequate cover for a while.