Planning permission is granted or refused by the council though, based on the need and impact on surrounding areas. A HOA can stop you hanging your laundry out to dry on a line, force you to water your lawn x times a week, prevent you painting your house a particular colour, prevent you installing a fence, determine they type of vehicle you are allowed and whether it can be parked on your drive or if it must be in a garage. It is not really comparable to planning permission which is really only required for significant construction work or change of use ie. Shop to residential or vice versa.

Plus if the HOA members don't like you they can make your life difficult. Planning permission affects everyone equally. If a neighbour can extend a property then more than likely you can too, if you are refused it is likely all similar applications would be refused, you don't know the planning officer and they don't know you so no bias can be involved which make the whole process much fairer.