I think we're getting some terms crossed. In my two-family home I will own the entire building. I will live in one unit and will rent the other unit to another family. So I (read: my wife) decide what color the building is. (This kind of owner-occupied arrangement is historically very common in my neck of the woods.)

So that's not an arrangement where both occupants get to control the building then. It's a situation where you get to control it, and if your tenant doesn't like it they can pound sand. It obviously does not address the scenario your parent is describing.

I would argue that (in the U.S. at least) there is an obvious and well-understood distinction between, "owning a multi-family home" (as the OP phrased it) and, "owning a unit in a multi-family home." The former is widely understood to mean ownership of the entire building (in every city I've lived in where two-, three-, and four-flats are common).

These kinds of buildings are not priced much higher (if at all) than single-family homes and owner-occupied arrangements (meaning the owner of the entire building occupies one unit in the building) are extremely common.

Does it matter that much? On my list of priorities in choosing a dwelling, if I'm allowed to change the exterior color is far, far down the list. I do in fact own a fully-detached house and I never bothered to change the exterior color, and nothing in my life would be any different if there were, say, an HOA in place that prohibited me from changing the exterior color.

Painting the house is a stand-in for having control over the building. You might not want to, but you might want to run ethernet or plant different plants or install a better dishwasher or any number of other options, which may or may not be possible depending on arrangement.

How would any of those other examples be prohibited in a dwelling that you own?

Look, I get it, you prefer a detached dwelling. But all the arguments you're making aren't compelling at all. It really sounds like it comes down to a preference thing for you.

Some duplex/townhome setups don't really let you do those things if they have something like a home owners agreement in place, which is sort of rare for detatched dwellings aside from some developments.

You get to paint your half. Unless their dwelling completely enclosed yours, I don't see the problem.

Now that you mention it, I actually have seen that arrangement before. It can look really cool if both people have complementary taste.

Sometimes you have a homeowners agreement limiting what you can do about the appearance of the property.