Thankfully there are more hits for "Courts Martial" than "Court Martials" which is the example I initially thought of. And google has learned to spell Cthulhu since I last looked.

Hm. Yes. I am of course in favour of using the traditional/correct/pedantic version of phrases, and pleased, and have always been taught to say "courts martial"[1][2], yet the alternative makes a lot of sense, as compared to many spelling changes apparently merely for the sake of it:

* If it's a noun referring to the court, then yes, "martial" is an adjective modifying "court", so the traditional reasoning holds.
* Yet, if it refers to the process, that isn't the case -- you don't say "his court" to refer to his non-military trial, so in "his court martial" "court martial" is a unit, not a noun and modifier, I think.
* For instance, I don't think anyone ever says "He was courted martial" rather than "he was court martialed". Or maybe we should.
* If it's a compound noun, or a compound word, there's a long traditional of just sticking an "s" on the end.

[1] Aren't there courts marital, too, come to think of it?
[2] See the whole "veils glaucous" essay, I wrote a whole mythology on the basis of noun-initial phrases :)

"courted martially", perhaps?

Of course, that just sounds like being chatted up by a squaddie.