Yeah, the article is written like it's parodying those who want to abolish timezones, but I'd be interested in specifically what you found unconvincing? I read the main point as being that time zones are an arbitrary social convention but that that arbitrary social conventions are pretty useful for humans.

Like one thing that the article does is repeatedly asking the question "but what time is it in Melbourne?" which I guess sounds pretty silly if you think timezones are unnecessary, since the question would be meaningless if timezones were abolished, and people in different parts of the world would already have centered their day around their respective parts of the clock and you would just look up what the times for everything are in another place. But I think the author was kind of already discarding that idea, because it's just equivalent to timezones - you have a lookup table for each part of the world to find out what people do at a certain time, except instead of being a single offset you have like a list of times like "school openings", "typical work hours", "typical waking hours" (?) etc. This system is basically timezones but harder to use for humans. So the author asking "but what time is it in Melbourne?" is in the context of this table not actually existing, because if it did, then you haven't actually abolished time zones.