It occurs to me that there is an analogy to be made between the development/ evolution/ extinction of martial arts systems and the same processes that occur in folk music.
Any song that exists was originally written by a specific person in a specific form. As the years go by, the following processes can occur:
The composer performs the song differently at different times, altering elements of the melody, the lyrics, or the style.
New musicians learn the song, but remember it slightly differently so that the melody and/or the lyrics evolve in different ways over generations.
New musicians borrow elements of one song and insert them into another.
New musicians make the deliberate decision to rewrite a song, altering the lyrics or the melody or the style or the instrumentation.
As a result, you can look around the world of folk music and find:
Songs that have the same melody but completely different lyrics.
Songs that have the same (more or less) lyrics, but different melodies.
Songs that tell the same story, but with the lyrics substantially changed around.
Individual lyrics or melodic phrases which have been transplanted into multiple songs which are otherwise completely different.
The same song performed in completely different styles - altering the final sound as drastically as completely changing the lyrics or melody.
It seems to me that you can find plenty of examples along these same lines in the martial arts. (I suppose in this analogy, the koryu folks are the equivalent of ensembles performing classical repetoire playing period instruments and using period tunings.)
From this perspective, whether you consider a given song or martial art to be extinct probably depends on your definitions. Is a particular song "extinct" if no one know exactly what the original melody was? What about if the lyrics to the chorus have been transplanted into half a dozen other songs over the years? What if there are two different melodies which are commonly used for the song and no one knows which (if either) was the original?
Just a thought. My brain is wandering in odd directions this morning.