I'm curious why none, or almost no mutual fund trades or hedges with options? Can mutual funds legally trade options? Are they banned by regulations?
Mutual funds are a major part of the reason a smile exists...yes, mutual funds hedge with options (and futures, CDS, and other derivs)
There are also a number of mutual funds (and I believe even ETFs) that implement a covered-call only strategy.
BXM is the SPX buy-write index, but I think it's a theoretical index and not tradeable. BEO is a tradeable covered call index, and there are others (FFA, MCN, BEP). But just like many other exotic etf/funds, there's going to be inefficiencies strictly due to scalability-- best to do CC's on your own.