I think that hypersonic interceptors would use a rocket motor and not a ramjet, but I'm not sure.

I think this is for offence because I understood the advantage of this engine (compared to a rocket engine) is that you don't carry oxygen so you can carry more fuel and get more range. I think range is much more useful for offence than defence.

I am possibly making myself look foolish now as I'm not an expert on either rockets or ramjets and I might have incorrectly dismissed defensive applications.

Historically, it was: https://en.wikipedia.org/wiki/Sprint_(missile)

Would be handy today.

That era of ballistic interceptors all relied on large nuclear warheads to have any effect.

The modern, hard problem is avoiding using a nuke, because detonating a nuclear warhead above your own country is Bad