I think what adds it a little more something to the Kinzhal is that it speeds laterally making it much harder to try and target with air defense. Maybe this allows for preservation of its speed and the kinetic energy can increase the yield of the warhead
Iskander was based from the outset to detect enemy radar sources... whether it is SAM search radars or SAM tracking radars or ARH radars in missiles like AMRAAM or Patriot, and it is intended to release jammers and decoys and chaff and also manouver around such threats that it detects on its way to its target.
Minor manouvers to evade incoming threats will cost in speed but it does not matter how fast you fly, if you fly a predictable course you can be intercepted, but even flying at half that speed but manouvering... and I am not talking 90 degree turns... just a few degrees one way and then a few degrees another way means the new shifted intercept point for the outgoing missiles is not moved dozens of kilometres in a fraction of a second with no chance of manouvering to compensate by the time you work out the new intercept point.
Basing the Kinzhal on the Iskander was easy and obvious because it is already designed for that role, and was already very accurate... by making it air launched from a MIG-31 it is like putting a very large solid rocket booster motor stage to get it up into the air and moving very fast before the normal motor even lights up.
Iskanders can carry tactical nuclear warheads so I would think Kinzhal could easily be nuclear armed if they wanted powerful effects on target too.
Most shipping targets would not require a nuke though... even the super carriers.
A Zircon launched from a MIG-31 will serve the same purpose as the Kinzhal.
Zircon is a combined rocket and scramjet powered missile... a ramjet or scramjet engine has a lot of empty space inside and on their normal rocket ramjet missiles like the SA-6 and Kh-31 and Onyx and Brahmos, that empty space is filled with a solid rocket motor to get the missile airborne and moving at speed so the air intakes can be opened and the ramjet motor started... it is a very simple type of jet engine.
Releasing such a weapon at 18km altitude and mach 2.4 flight speed would mean the solid rocket booster... instead of getting the missile moving and through the thickest air at sea level to where the jet engine can be started to accelerate it to higher altitude and higher speed... it can accelerate the missile to even higher altitudes and even higher flight speeds.
The Kinzhal is a solid rocket so power is fixed... it can't throttle up or down... when it reaches its top speed any extra thrust is wasted, but with Kinzhal when it gets to its top speed it can throttle back and reduce fuel use and therefore travel much further.
Being launched from an aircraft boosted the Iskanders speed from mach 6-7 to mach 9-10, and its range from 500km to 2,000km.
The Zircon wont get as much range advantage but it will probably boost speed to mach 11 or 12 perhaps which will likely at 500-1,000km to its ground launched range of 1,500km...
The only reason Kinzhal exists is because too many Iskanders have been produced and so someone came up with this idea of strapping it to an aircraft. The U.S toyed with this idea of an air launched ballistic missile back in the 70s but dropped it in favor of ALCMs.
Iskander is much better designed to evade enemy air defences... it does not climb and accelerate to speed and then burn out and then just fall back down to hit the target... it levels off and flys to the target like a plane and its flight is powered all the way like a plane so you can't just calculate its trajectory like a rocket, you have to track it and chase it like a plane... but it is much faster than any plane.
An air launched version was a very quick and easy way to get an effective weapon in service quickly and cheaply.
A US ballistic missile would not have been as useful because it would be as easy to shoot down as their ground launched missiles at the time... or for that matter a Soviet Scud missile or FROG-7 rocket...
Kinzhal might carry a few decoys but it is in no way better than a Zircon. In other words, there is no need for a Kinzhal when the Zircon already exists.
Kinzhal is available and cheap and already in mass production... they can keep using it for quite some time.
Zircon is more sophisticated and faster and could be launched at lower altitudes and lower speeds and still be very very capable... and being longer and slimmer rather than short and fat it would be easier to carry on weapon pylons or internal rotary launchers in large numbers.
Zircon is designed with decoys and sensors and to evade enemy air defences too, but optimised for naval defences... which ironically are the strongest the west has in service and the only air defences that approach the performance of Russian AD.