Well here's an economic application without nuclear tipped warheads.
The Wiki pages says top speed is about Mach 4. There are already multiple rockets from US, Russia, and China that can achieve the same (or more) but with a solid-fuel rocket motor. What is the advantage of a ramjet here? It just seems way more complex and much less well tested (in labs and in combat). Also, has this missile (Meteor) been used in any combat scenarios? To be clear, the max speed for any fighter jet is about 2.5 Mach. Once one (or two) of these missiles has locked on, you are done. I read some funny commentary once about how to shoot down a modern fighter jet: Two missiles. They can dodge the first one, but sacrifice so much speed, that the second one can easily find its target.
A ramjet drastically increases range against maneuvering targets. The 'maximum range' quoted for missiles like the AIM-120D (Likely 140-170km) is normally for a front on shot at extremely high altitude (10-15km+) with no evasive actions. With an evading target the No Escape Zone (where a target likely can't kinetically evade the missile) will only be 15-25km.
The Meteor has a longer sustainer and a terminal boost meaning that the No Escape Zone is though to be upwards of 60km. Qatar might have used Meteors to shoot down Iranian Su 24's just a few months ago based on the range they were shot at.
It's not that simple. If the target aircraft is outside the minimum abort range then they can still evade multiple missiles, regardless of whether the shooting platform or the missiles themselves are locked on. Typically they would do so by descending into denser air and beaming the missile to bleed its limited energy. On larger missiles a ramjet can potentially allow it to retain more energy into the terminal phase.
There are a variety of other defenses including countermeasures, signature reduction, EW, and decoys which also complicate the issue.
Missiles versus aircraft is a fight between very high kinetic energy in the missile, and relatively low kinetic energy in the plane, but with the ability to generate more kinetic energy. Missiles don't have a lot of fuel, so they need to generate a lot of kinetic energy to still be effective by the time they reach the target. Typically a missile will accelerate to its top speed in the first few seconds of flight and coast the rest of the way. At very long ranges, all the energy generated when launched has bled off, so there's two common solutions for long-range missiles to generate more energy: a "dual pulse" motor is basically a second rocket motor that fires later in the course; or a ramjet, which can be throttled up and down and is more fuel efficient than a rocket engine.
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