The Russians are also in Syria sitting in their port... They have the SS-N-22 Sunburn, it has been called the most lethal missile in the world today.
Iran also has these, perhaps Syria as well.
Never underestimate the other side.
The Sunburn can deliver a 200-kiloton nuclear payload or a 750-pound conventional warhead, within a range of 100 miles, more than twice the range of the Exocet. The Sunburn combines a Mach 2.1 speed (two times the speed of sound) with a flight pattern that hugs the deck and includes violent end maneuvers to elude enemy defenses. The missile was specifically designed to defeat the US Aegis radar defense system. Should a US Navy Phalanx point defense somehow manage to detect an incoming Sunburn missile, the system has only seconds to calculate a fire solution not enough time to take out the intruding missile. The US Phalanx defense employs a six-barreled gun that fires 3,000 depleted-uranium rounds a minute, but the gun must have precise coordinates to destroy an intruder just in time.
The Sunburns combined supersonic speed and payload size produce tremendous kinetic energy on impact, with devastating consequences for ship and crew. A single one of these missiles can sink a large warship, yet costs considerably less than a fighter jet. Although the Navy has been phasing out the older Phalanx defense system, its replacement, known as the Rolling Action Missile (RAM) has never been tested against the weapon it seems destined to one day face in combat.
So we kill people who kill people and both sides want to kill us. What’s not to like?
Your post assumes that the USN will approach within the Syrian missile envelope, which they will not.
Also, if anyone unleashes the canned sunshine, all bets are off. The American public would demand full-scale retaliation, and Oshitbag would piss himself and cry.