In Libya, Fr. UK, and US did the right thing.

But Arab League support depended on the US letting the KSA crush the Arab Spring in Bahrain first. (as KSA is now doing in Yemen).  It was a devil's bargain that made America complicit in crushing democracy.

Wars consume vast quantities of resources - arms, money, and fighters.  Mercenaries don't come cheap.

In Libya, once Kaddafi was gone, our supposed "Allies", chiefly KSA, set about making the revolution fail.  Their unswerving objective in all these conflicts is to prevent democracy from being established in any Arab country - an outcome viewed by KSA as a mortal danger.

They would most like a compliant puppet thug.  But if not, total chaos that discredits the Arab Sprig serves their purpose - if it sets off a refugee wave, so much the better.  That will teach the Europeans that a known tyrant is preferable. to their meddling.

The result is the current proxy war in Libya:

NATO (democracy) v. KSA + Egypt (anything-but-democracy)