I guess it's because Urizen did it on purpose. So he made sure to receive as much power as he could by attaching itself to the tree. We already know that the method Urizen used is not the only one to get power from the Qliphoth. Nidhogg for example does it through parasitic infection (which is different from Urizen's way cause Nidhogg physically needs the tree and can't leave it without dying, whereas Urizen can do whatever he wants). Dante apparently, through sheer luck and unbeknownst to him, found another one, entering his own state of temporary "symbiosis" with the tree, which kept him alive during the coma.
I don't even think it was a "powerup", just a life support.