To my view it looks more like an attempt to inflate a minor controversy by excessively documenting it. If this much effort were being put into writing about government policy I'd totally agree with you, but this level of detail is uncharacteristic even for Wikipedia.
> That being said, there should be absolutely no regard for "sensitivity" or the fact that Musk is a living person
Wikipedia always had particularly strong rules about how living persons are supposed to be covered. I wouldn't agree with making exceptions just because I dislike a powerful individual.
In terms of leaving the page up: I don't expect Wikipedia to be censored, but looking at this page the content unavoidably comes across as something that'd only merit a couple of lines on the main article. Instead you have a literal essay just to record "those aligned with the left believe that Musk made a Nazi salute, those aligned with the right say that he didn't".