Probably because it’s unclear what this pedantry about synecdoche contributes to the discussion. Many people (including journalists at the state broadcaster) happily refer to the whole tower as Big Ben, so that is functionally one of its names.
Is the fact that the name originates from a bell, and that the official name for the tower is different, interesting? Maybe. Is it worth “correcting”? No, for the same reason it’s not worth policing people’s use of “Google” to mean “Alphabet”.
While I'd typically agree that pedantry is normally rather boring, the pedantry in this case is actually interesting in that the individual properties of the object have their own name and are addressable uniquely. It sounds like they are public as well.
I also reject your premise this is anything similar to referring to Google/Alphabet as interchangeable.