In our WA county there is ONE badged game cop. He spends his time on the highway next to the Columbia or roads along tributaries checking hooks, stringers and of course licenses. He doesn't have to walk too far to justify his existence.
But in the remote woods whether its a trespasser hunting and poaching or a predator like a bear or big/little cats tearing things up and killing animals he is useless. Even a dead and obvious diseased coy or deer. So any call goes to the Sheriff and they absolutely respond based upon risk and obviously time of day. Even with dog teams if needed. The Sheriff's office will make the contact with WDFW and somehow that works better, go figure.
There was a knock down drag out a few years back between the Sheriff and WDFW. WDFW was challenging deputies for solving problems that should involve a game cop. Again, based upon risk at the moment and the ultimate local authority, guess who won the argument?
But, in a previous time in a different county also along the Columbia, there was the one badged game cop there also. That guy seemed to be where he was needed and if not in a surprisingly short time. He was helpful++ but stern for screw ups and violations within reason. He retired. I hope he is living his years out well having done excellent public service - he earned it.