Wondered whether this or the MENA thread is more appropriate, but I think it's more relevant here.
Turkey vetoes Israeli participation in a NATO exercise.
This actually isn't the first time. Israel also had dialogue with NATO in the past about whether it would join and on what level (not necessarily full member). Israel does participate in NATO missions when required, and is a member of the Mediterrannean Dialogue. And it participated in some exercises as well, including on European soil. But Turkey put its effort to torpedo all connections between Israel and NATO.
Now, I'm NOT saying the US is going to leave NATO. To the contrary, I think the US stands to benefit a lot from it after the reforms pass.
But it would also be wrong to look at NATO as this rigid, eternal solution to the north atlantic problems.
Intertwining alliances between member and non-member nations could allow members to retain their sovereignty and still benefit from the alliance.
One possibility for the MENA/Mediterrannean region is a bloc containing the US as sponsor, and Greece, Cyprus, Israel, as the core. And other members being Italy, Morocco, Egypt, Jordan, Saudi Arabia, UAE, Bahrain.
If EuroNATO were to help form such alliance and co-sponsor it with the US, it could better maintain interests in areas outside its zone of control, without spending disproportionate treasure and overstretching its forces. For example, such alliance could utilize local forces to meet challenges in the Red Sea and Persian Gulf.
India and France are potential observers who'd be interested in the outcome of such endeavor. France has cultural influence in Morocco and ties to Egypt, and Lebanon which neighbors multiple potential members. India stands to benefit from increased energy security.
Other potential alliances could be formed if NATO is not disbanded, but culturally downgraded. For example it can be argued that the defense of the small baltics, deterring Russia, and collective defense - are all similar but somewhat different missions that may require different levels of attention and resources, in turn putting different responsibilities on NATO members depending on geography.
The theoretical alliance I described earlier is a straight geographical line going from the west med to the gulf.