That's not the original intent. In the US, HOAs were mostly created after the end of segregation to keep black people out of white neighborhoods, an origin story that puts into context the modern of pettiness and desire to control others we see in stories like this.

In the early postwar period after World War II, many [HOAs] were defined to exclude African Americans and, in some cases, Jews, with Asians also excluded on the West Coast.

A racial covenant in a Seattle, Washington, neighborhood stated, "No part of said property hereby conveyed shall ever be used or occupied by any Hebrew or by any person of the Ethiopian, Malay or any Asiatic race."

When these were found unconstitutional in 1948, they became private contacts until those became illegal in 1968, but because HOAs had to approve new members/buyers, the rules stayed in effect until the majority of a community decided to stop being racist. On top of that, in 1963 the Federal Housing Administration said they would only insure mortgages on homes with an HOA which is really what created suburban sprawl and the ghettoization of the American inner cities.

If you look at the history of HOAs it's really a long and protracted fight on all levels by racists and bigots against the Civil Rights movement.

 https://en.wikipedia.org/wiki/Homeowner_association

TL;DR: Although conceptually HOAs are a good idea, even trending towards communalism, actually existing HOAs are, with a few exceptions, downright regressive, often criminally so.