Not true. All major clients support at least 1.16.5.
That depends what you consider a major client - CaloriMod, the client I, along with a lot of others, use, does not currently support 1.16.5 for example. This isn't a "major" client if you look at all of Java, however that's because it's Cube specific, looking at the Cube community alone, it's a very popular client.
CubeCraft is already working on it.
...They're not? The original thread I assume you're talking about said it "doesn't mean we won't be considering it in the future". It did not, at any point in that thread, say definitively they would be doing it, much less that they're already working on it.
I'd also like to point out that, while the data provided in the thread may be very outdated, it can still be used as a very rough reference point.
At the time of the deletion of previous versions (1.9 - 1.11) the total number affected was 64, between all the versions. That's compared to the (at that time) 300+ players of 1.12.2. Updating to even one version above 1.12.2 would already be affecting more people than were affected in the entire previous udpate removing several versions.
Obviously having access to newer data the Cubecraft Team might still come to different conclusions than us with our very limited and mostly outdated information, however as I see it currently, with the information I currently have, updating does not seem like a good idea.