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

Ecological and economic damage can reverberate through ecosystems when invasive species become established — and some such as oak processionary moth caterpillars can cause physical harm to humans and pets

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.