Are there benefits for using Static Diffie-Hellman over Ephemeral Diffie-Hellman?
The "advantage" of static DH is that the server doesn't need to compute an exponentiation each time. This advantage is, however, not worth it, in the sense that the static DH problem is easier than the DLOG problem (to the best of our knowledge). In the paper The Static Diffie-Hellman Problem (PS) by Brown and Gallant, they show an attack on the static DH problem for Elliptic curves that is significantly faster than the best known for ephemeral DH.

Note: I would not call static DH "standard"; on the contrary, in my mind, ephemeral is the "standard" version.