I am not sure how it works in your company, however in my they always choose the lowest rate available, taking the risk of paying the change fee if needed. My opinion as a passenger is not taken into account.
A real life example from a flight I need to take next week to Bangkok - price difference between S to Q is $300, and another $150 between Q to K (after the corporate discount). That's sums up to $450, so even for any other corporate its reasonable to take the risk of paying $170 change fee if needed.
I don't know when was the last time you checked availability... this month's flights are empty, for example I cheked today the availability of K class seats on the Saturday night TLV-HKG (a flight which is usually so full) and there are more than 10 seats on T (loest class, but requires a minimum stay so irrelvant for most high tech travellers) more than 10 seas on K and more than 10 seats on Q....
So I'm sure many companies will start booking the lower fare classes soon and means we'll loose our status, we won't get upgrades, and practically we won't have any good reason to fly LY....
I think we should put some pressure on LY to allow last minute upgrades on K and Q, and consider increasing the points on K (or any no minimum class) otherwise they'll loose us as passengers....