People need different metaphors. So it's often good to present students with a slate of them; if one doesn't work, try another.

It's important not to get stuck on the metaphor, but in practice all but the weirdest of us need them to bootstrap into a mathematical intuition.

This one does absolutely nothing for me either; even casting my mindset back to when I first encountered the episilon-delta treatement I don't think this would have helped me. But if it helps others, that's great.

Also, I think this is a concise treatment. If I were to try to present this to a math class, I'd expand it into at least half a class session, if not a full one. Terry Tao is presenting the metaphor fairly directly, not for pedagogical purposes on this post itself. If 3Blue1Brown took this post and ran with it I'm sure a lot more people would find the result useful at that density of presentation.

Increased precision typically costs more economically, so I think it's a pretty good analogy... precise physical measurements require specialized equipment, precise floating-point calculations require more computational power, etc