Golf courses, at least the ones I've been to, have tons of trees. They're usually densely forested in the areas between holes to make a sort of barrier. And I certainly see more wildlife on a golf course than in, say, the parking lot of a strip mall.

I found a squirrel's nest on one course with about a hundred golf balls in it. And I've gotten chased off my tee shot by a bull elk.

not all suburbia is north american ffs

Look at what people in NYC and north east NJ call suburban, then look at what someone in upstate NY calls suburban. Density is very different. Look at it as a scale. Dense Urban, Urban, light urban, dense suburban, suburban, etc. I am specifically pointing at places like in NJ where it would more likely be turned into a mall than a park.

Many towns have public courses which are just as described.

Ideally sure, but we are dealing with capitalism. In a high populated area people will want to find a way to profit over every inch.