Why use minhash instead of directly computing Jaccard coefficient?
If you only have two sets $A,B$, then you are right: there is no point computing the minhash.

But now suppose you have sets $A_1,A_2,\dots,A_n$, and you want to know whether there exists any pair $A_i,A_j$ with high Jaccard similarity.  It's more efficient to compute the minhash of each $A_i$ once, and then use that to help you look for a pair that hash high Jaccard similarity.  As a trivial observation, once you've already computed the min-hashes of them all, then estimating the Jaccard similarity of $A_i,A_j$ can be done in $O(k)$ time using the existing minhashes, which can be significantly faster than the naive  $O(|A|+|B|)$-time method.

(In fact, once you have the minhashes of all of the sets, there are even cleverer ways to look for pairs $A_i,A_j$ with large similarity.)

This is even mentioned on the Wikipedia page for Minhash: see the section labelled Time analysis.  However, you do have to read it pretty carefully to get the point.