The USA is currently being governed by a madman. Looking for for reason or rationale behind any of his decisions is a waste of time and effort.
There was no reason for Trump to invade Iran. He himself changes his explanation for the war and its endgame almost daily. He did it because he could. He did it without any consultation with his NATO allies. It is not a NATO operation, it is entirely an American operation.
Ttrump is, of course, now blaming NATO allies for not following on and causing any defeat, but they were never asked or consulted about the war, why should they take part? A few have offereda bit of help, and British planes are helping to defend the Gulf States, who are collateral damage, but, why should NATO members risk men and materiel in a war they were not consulted on and do not want?