How would it be beneficial?
How would it not? You get one more person on your side of the table in the event of Bad Things, one of your major members doesn't have to worry about Sicily and Naples getting spontaneously shot up, and your southern flank will now be as secure as it can be made.
For Libya it is an effective means of assuring that the EU and the US have a vested interest in the prosperity and stability of their nation, as well as assurance against opportunistic or unstable neighbors who might want to export their problems; Chad comes to mind.