Have had no problem with species baptisia or the cultivar Cherries Jubilee. Have them hemmed in by other tough competitors, like New England asters. Have not seen them seed but do cut them back to ground level, along with the pods, by the end of the growing season.
Think there's numbers of plants, with various degrees of relationship, that can be called Joe-Pye weed. Have had two white snake root ''Chocolate' plants, going for years, with no problems. Picture was from last weekend.