I understand what you are saying, but growing up the term 'weed' was always used in the 'undesirable plants' sense and the term 'invasive species' is more accurate when you are discussing them specifically. When I first started gardening, the guy who trained me defined weeds as 'any plant the client doesn't want growing on their property'.
Stuff like dandelions and such.
Dandelions are a complex topic. While some consider them "Noxious Weeds", other people recognize their value as important sources of food for insects, they attract pollinators, and they also release ethylene which is a gas that encourages fruit setting and fruit ripening, so they are sometimes grown as 'companion plants'.
Dandelions are only weeds if you don't want them there, like any other 'weed'.
HOAs are the invasive species