Actually, it's the liability of "doofus brings a lawnmover to the park and cuts off his own foot with his own lawnmover, then sues County and wins" that causes parks departments to risk manage those sorts of clauses. Hiring an actual bonded landscaping company to mow might be allowable. It might also suck the entire RCF budget dry, so it's probably not an option anyway.
Back in the day Creve Coeur was kept up very well, but after the flood at some point the course was designated as flood plain and was dropped to the lowest mowing priority...basically it got mowed after everything else was mowed and they had run out of things to do. That didn't happen very often. As bad as the grass is now, it actually seems to get mowed more now than it did then.
This is one of the unintended consequences of who we are. We get pretty free reign to do our own thing on the County courses. If we didn't have so much control and the County ran leagues and tournaments and charged admission to play, the grass at CC would be cut. In a "big picture" sort of view, long grass as CC is a small price to pay for all of the control we are given at these courses.
It still sucks when you throw your disc in the middle of the fairway and can't find it in the long grass. I wonder how many discs they grind up when they do mow?