Golf courses also get de-facto tax subsidies under a property value tax, because they're basically empty lots.
If you bought that golf course and built something productive that produced value for the community, like apartments, detached houses, a factory, a store, anything at all, you'd suddenly have to pay more tax on it.
A land value tax would push golf courses further from city centers.
I have never played golf but why do you say it does not produce value for the community? Why is it better to have homes at the cost of lost recreational space?