The idea is supposed to be that an HOA can be more efficient in taking care of problems. The municipality can be underfunded, etc, and take a long time to solve a problem.
In practice, HOAs generally don't do anything useful, though.
That’s always the pitch when privatizing government functions. It rarely works out.
Our neighborhood actually saves the County money for property they don’t have to maintain (drainage/swales/mowing/etc) and provides community things like tennis courts, basketball courts, pools, playgrounds etc that the County doesn’t have to provide or maintain. It’s also cheaper for the HOA to do it