I loathe the Himalayan Blackberry. The berries, while large and numerous, are bland. They store a lot of energy in their roots quickly, so once they get a foothold, they send out shoots everywhere- especially after you cut them back.
Goats are the best remedy. I had a single goat clear an acre of 8-10' tall bramble in a span of a few months. For good. They eat new shoots as soon as they appear until the blackberry roots have expended all their stored energy.
If you don't have a goat, then you must remain vigilant. I have a zero tolerance policy towards blackberries. If I see one on my property, it dies.