There are butterfly bushes and butterfly bushes. Aren't a lot of the newer varieties sterile? I grow two of the smaller, newer varieties and one old variety, White Profusion. Personally, I have never seen a seedling of a butterfly bush in my garden in all the years I've grown them. I do usually dead head to help encourage new blooms but there are always a few spent blooms I can't reach and remain on the plants. Also, I don't usually trim the last growth of the year until the following spring. Seems like a seed dropped from these last bloom heads would have germinated at least once through the years. These plants produce some of the best nectar blooms I have. The butterflies, hummingbirds and pollinators flock to the blooms. I would hate to be without them but would remove them if I thought they were destructive to my environment. In my area, they have proved to be a wonderful addition to my butterfly garden and behave very well for me.
On the other hand, ask me about Rose of Sharon.
These plants are some of the most easily spread plants by seed I've ever encountered. I've pulled hundreds of seedlings and cut back umpteen new plants started from seed scattered in my garden via the neighbors Rose of Sharon plants. Now that plant I can do without.
Myles