Exactly, and that's not even that unusual in terms of the 20th century, e.g. I believe Desert Storm was officially a UN force as well. The book discusses a lot of examples of people talking about sending UN troops somewhere and that either happening or not happening (and often, it happened!)
I think it is maybe only after the Iraq War that people stopped thinking of the UN as an alternative to conventional war politics. IIRC, Bush acted unilaterally without UN approval, and now it kinda seems like the "you should get UN approval before making war" norm has been lost? I don't remember anyone even discussing the possibility of UN approval for any more recent US military actions like in Libya. And the UN hasn't played a large role in Ukraine either -- I suppose that might be because Russia is on the security council?
I think it is maybe only after the Iraq War that people stopped thinking of the UN as an alternative to conventional war politics. IIRC, Bush acted unilaterally without UN approval, and now it kinda seems like the "you should get UN approval before making war" norm has been lost? I don't remember anyone even discussing the possibility of UN approval for any more recent US military actions like in Libya. And the UN hasn't played a large role in Ukraine either -- I suppose that might be because Russia is on the security council?