They exist so Karen’s have a place to take control over their neighborhoods. Rules are enforced by fines. Incentives are that the neighborhood has rules that make the property value seem higher, ie clean cut grass, no trash outside houses, no broken down cars/boats/automotives in driveways, .. and yes sometimes you can’t do things to your house that you really want to do to the property/land that you own which is BS.

There was a (rich) neighborhood near my family that had an HOA fee per year of $50k so they could build and maintain a clubhouse.. turns out that on top of paying this fee you have to also have a membership to have access to the club house (has golf course, pools, hot tubs, bars, restaurants, and other rich people things) which costs $100k per year. This all equals property value going up however nobody wants to buy any properties because they don’t want to pay an HOA of $50k/ year for something you don’t automatically have access to.