Can a constitutively active kinase be highly regulated?
I think you have answered your own question, but yes, the nomenclature is confusing. When they say it is a constitutively active kinase, you are right, it plainly means the enzyme can always phosphorylate other molecules/proteins.
The regulation part is what you have in the review paper you cited. If the kinase is always on but localized in a compartment where there is nothing to phosphorylate, it could be considered &quot;regulated&quot;. The same logic applies to the other regulation methods listed.