Agree that mowing after the seeds are ripe would not be very effective as a means of controlling it, but if that's all one has time for instead of pulling, it would help a lot.
I'm sure all plants have some value, and buckets of chamberbitters are a great addition to compost, but this is not one that can co-habitate with other plants of small, ornamental stature.
I'm intrigued by the tea. I find the smell of this plant unpleasant.