This idea certainly looks good on paper, but it would be a major operation to take control of all ports in Lybia. With a serious risk of casualties for NATO troops.
There will be some NATO casualties for sure, if the rebel groups (especially the Islamic State) engages them. But since the NATO is a superior fighting force, they will be able to pull off this operation with minimal losses. The rebel groups are fighting against each other, and this has made them very weak, in terms of manpower and equipment.
Any loss of life makes terrible news. In EU or US, nobody cares about the death of a Palestinian or a Syrian, but the death of a western soldier immediately makes headlines, and that's bad. You see the opposition asking about the reasons behind the sending of the troops, and calls to bring the boys home. I'm afraid no government from a leading NATO country is ready to accept that.