Even in places where they thrive it is good practice to cut them back hard in spring every few years. They are very ugly twiggy bushes and look much better with regular rejuvenation pruning. It might be useful when trying to keep them happy to think about where they come from. Their natural habitat is in China where they grow in forest clearings, riverbanks and limestone outcrops. So they prefer lean, fast draining soil but with plenty of moisture at the root. They are a woody weed here and are particularly prevalent along railway tracks (they like the ballast), quarries, urban wasteland and disturbed areas. I agree with Ken about the butterflies. Although Buddleja attracts adults to the nectar they are not a food plant for butterfly larvae and so they do not provide a good all round butterfly habitat.

Embothrium (Pugetopolis)... actually we did inherit this shrub at our new home. We bought the house in February when the grounds were covered with snow. The original owners had moved out the previous summer, so there was no winterization or prepping... and lo and behold, we found 8 gardens when we thought there were 3; and a lot of plants/bushes & trees we had to reach out to identify. My husband tried to do a bit of 'spring' cleaning this fall and we probably should have left this bush as-is. It didn't bloom much this year (probably due to the unnecessary pruning. I'd take the fact that you thought this was a public garden as a compliment, but really? I've had nothing to do with it, it was all the previous owners work that we're enjoying now. We decided this year to see what the gardens had in store for us before making any decisions on management and changes to the gardens. So, next step, I guess is to go off and try to find the brush section of the forum to get more insights into helping a couple of the bushes we're enjoying thrive.

Yeah, of course. Not sure how I missed that, as I'm also growing Black Lace (although not very successfully between the deer and probably verticillium wilt)

Not a plant I know from personal experience but compare with Baccharis halimifolia.