In fact, the federal legislation that charges the Federal Reserve with supervising bank holding companies - the Bank Holding Company Act of 1956 - was enacted in large part to prevent the affiliation of one of the largest banks in this country with a large insurance underwriter.
The stability consideration comes from the point that I made at the outset. The purpose of promoting central clearing is to reduce systemic risk. CCPs reduce risk in one important respect, but they also concentrate it in a specific location.