Even 'pretty' invasives are not welcome for very good reasons

Impatiens glandulifera — Himalayan balsam is a high impact invasive species that causes significant damage to the ecology of both terrestrial and aquatic habitats
Himalayan balsam is a beautiful flowering plant, introduced into ornamental gardens for its vigorous growth and abundance of bright pink, bell-shaped flowers through the summer.
But having escaped in to the wild, Himalayan balsam has now conquered huge swathes of river banks, parks, gardens, and waysides, leaving no room for native wild plants or their associated butterflies, hoverflies, moths and more.