Of course the proposed military action here is launching cruise missiles from ships in the Med to hit targets within Syria. How many NATO or allied countries even have that capability?
The UK and the US, but France can launch missiles from aircraft outside its airspace.
Exactly. Six countries provided troops for the US invasion of Iraq, because every country with a military has troops, so it's not like there was some fundamental limitation on who could participate. But in the case of Syria, the military action in question is something that most allies of the US lack the technical ability to participate in, which is why it's only the US, UK, and France who were ever even considering it.