Why would anyone use an elliptic curve with a cofactor > 1?
Montgomery and twisted Edwards curves have even order, but the group law can be implemented using fewer multiplications than Weierstrass models.  So that is why these curves are popular and we have to live with cofactors $&gt; 1$.

There are other reasons to prefer to use prime-order elliptic curves (e.g., small subgroup attacks).  So you are right that in an ideal world one would used prime order curves.  But sometimes it is worth the trouble to use a more efficient curve model.