Why should I prefer tea dust over crumbled tea leaves at home?
You don't necessarily want tea dust. The reason commercial producers grind it so fine is to maximize the flavor output and steep speed with the least amount of tea, but and this is my opinion only, I think that makes an inferior tea.

Good tea just uses more leaf so it can reach the desired richness in less than 5 minutes.

Steeping for longer draws more tannins out of the leaf and woody bits and makes tea more astringent, and so does grinding the tea too finely.