If OW would have them they would join in a heartbeat is my guess. Lan Chile might not be too excited about the idea.

MX were full Star Alliance partners until pretty recently.

I've flown MX quite a bit and they are pretty decent for a Latin based carrier.

I always smile when reading a carry on tag I have from a couple years back:

Clase Ejecutiva

Pasajero Distinguido

The other side is even funnier:

Distinguished Passenger

in large black letters.