The size of the alliance is also important in the sense that it will not allow any nation to be isolated internationally should a war take place.
You see if Isreal were to start a war against Turkiye tomorrow, they would move to isolate Turkiye internationally using the influence and power of the USA. This isolation will come in the form of economic and political sanctions, embargoes. These sanctions/ embargoes are what is really holding Iran down. If the USA were not able to apply them to Iran, their situation against Isreal would be very different.
But if the defence alliance were large enough, it would be hard for the USA to target one nation without risking losing the entire bloc. A risk that would be simply too large for the USA to take.