Further erode relations between Israel and other ME countries.
Turn international political option against Israel.
The only path to any kind of resolution in which Gaza gets sovereignty is if Israel is forced to the table by the international community.
To do that, Hamas has to get Israel to kill as many Gaza citizens as they can
President has wide latitude in matters like this. Air strikes in this context are legal for him. He can even deploy troops as long as their deployment isn’t longer then 60 days.