You definitely need that level of governance if there are common elements which need to be funded and maintained (pools, parks, the building itself for condos)
Only in a very minimal sense. A management that is only empowered to maintain common areas of a community can't "govern" the community members except in the very narrow sense of enforcing whatever rules the community wants to have for the use of common areas. Which is just an aspect of the fact that the community as a whole owns the common areas and the owner makes the rules.
Such a management can't mess with community members about how often they cut their lawns, or what color they paint their house, etc. But that sort of micromanagement is what "governance" by HOAs ends up being when it goes beyond basic management of common areas.
Sure. I think very few, if any, people dispute that. If there actually are common facilities like pools, it makes sense to have a common pot of money everyone contributes into, to maintain those facilities. Just about everyone will agree with that.
How do you make the huge leap from that, into saying a HOA has any kind of right to demand what kinds of flowers or windowshades or decorations someone installs into their private (not shared!) property?
This varies widely depending on the city. In many cities, it's hard to find a detached house in a neighborhood (that isn't ghetto) that doesn't have an HOA.