This is the logical thing to do for most people. If one is forced to stay at other chains for official travel, why would one not consolidate leisure travel to that chain? Except when someone is trying to achieve status with more than 1 chain. Perhaps Marriott loses money on government rates, but I thought it's often not available if occupancy is high.
LAX
I don't think hotels are losing money on government rates unless it's a sell out during a time they can charge a premium like the pebble beach concours, the superbowl, or something.
In CA, CA state rates are open to leisure travel unless otherwise prohibited. I almost never see the "official travel only" disclaimer anywhere except in around around Fresno during peak Yosemite times. There are a few other hotels that only list state rates on the concur (and not Marriott), which we aren't allowed for personal use. Honestly I see enough weekend state rates that I think many hotels are actively targeting state employees, at least on non- peak weekends.