First of all, I've heard that these policies are getting rarer and rarer. My company implemented one for a very short period of time, and then just switched to "get the lowest fare" as the policy. The concept of a "Preferred" carrier no longer exists to any great degree.
Having said that, I have always flown major airlines, collecting miles, status, and upgrades. I do a pretty good job of seeking out the lowest fares AND getting my company a good deal. Sometimes I even go out of my way to take an earlier/later flight than required by policy to save the company a few hundie. It's a win-win. They don't throw Southwest or Vanguard in my face, and I am conscientous about sniffing out good fares.
But hypothetically-speaking, if my company offered this option, I'd say my openness to accept it would vary by situation. Specifically: what is my risk that I will require customer service from the (non-status-for-me) airline? For a nonstop flight, no checked bags, low risk of me needed to alter the ticket, and a good ontime record, I take the money if it's the situation described above. (~$450 after-tax in pocket vs. ~6,000 status/13,000 total FF miles) Exception: It's December and I really need that AA flight to reach the next elite level.
However, if my itin included connections, a good chance I would need telephone support at some point, or any scenario that required a wait at the check-in line, I probably don't gamble. I take the AA flight.