Often invasive plants aren't desirable in natural settings if they've been introduced by human activities, such as from the early settlers. Sometimes his has been intentional, other times unintentional as seeds are inadvertently transported on cargo and in ballast of ships. Native plants are defined differently by different groups, but generally are considered those plants found growing in an area at least 100 to 300 years ago.
Exceptions seem to be areas, such as forests, that one species, such as maple, dominate.
But even then, if you look closely, many other species of plants may be present. It often displaces and kills other native species that certain wildlife need to survive. Loss of native species sometimes leads to a wildlife species becoming endangered or extinct. Invasive exotics may completely change a habitat, especially in the case of wetlands. This is where invasive plants are often found, as the seeds and even root and plant pieces are carried down streams and into lakes by the water.