You are being obtuse. It seems obvious from your posting that you have a 'keep the riff-raff out' kind of mentality about the 'amenities'Wtf discrimination dude?!
Private property should be used by the public?! Bull buddy, bull on that....
Generally, in the days before HOAs apparently became a thing, you would own the pool and a tennis court or two because you built them on your property or bought a house that already had them. Paid a bit more up front but no 'dues' in perpetuity and you could paint your trim any color you wished