1st How an interceptor missile works?ESSM is designed for stopping supersonic and subsonic cruise missiles and low speed aircrafts. It is especially good against sea skimming missiles. It was never designed against ballistic missiles.
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Mission/Role:
The mission of the ESSM is to provide the U.S. Navy and allies of the United States with a missile with performance to defeat current and projected threats that possess low-altitude, high-velocity, and maneuver characteristics beyond the engagement capabilities of the RIM-7P Sea Sparrow.
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Although real range and altitude figures are classified, ESSM is thought to have an effective range of 40-50 km . it can not go too high in altitude either - just check our Gokdogan/G40 if launched from land-. With that sort of range and altitude it would be a real feat of achievement to hit a target like Bora which will cover that 40km within 20seconds. Also if it was vertically trying to hit the incoming Bora, an ESSM will not even make half that distance.
Logically, like you say, if vertically launched and had enough juice in it like a booster, it could be able to intercept.
Also the targeting radars of ESSM will have to be able to lock on to the maneuvering and altitude changing Bora in the first place.
Bora will be detected far before than 40 km distance, nearly max distance of search and track radar, ESSM will have enough time to intercept with a predicted route. Block II has active rf seeker for terminal stage which wont rely on the ship for illumination in that stage.
The low altitude does not only refer to sea skimming missiles. It depends on flight profile of Bora but it wont be exactly vertical too.
2nd Bora as other ballistic missiles doesn't have any maneuvering ability. It follows an easily predictable path with corrections for guidance, easy to keep radar lock on. ESSM will not need to maneuver for that, probably effective range and altitude may increase.
What is the advantage? Possible threats which Bora might be used against is not acquainted with such a threat. ESSM and other self defense systems are rather optimized for near surface threats (or up to medium altitude for ESSM) but still useful against, yet operators is not trained for that.
It is not the same for a sea skimming HS cruise missile which is detected rather late, leaves a little response time.