I personally think there's a weird disconnect between 'kata for conditioning', 'kata as story book' and randori.
It's conceivable that lots of folks mish-mash things with different purposes together.
Would you try to 'beat someone up' with deadlifts, windsprints etc...or would you use the attributes those things imbue to improve your randori?
Perhaps then - viewed in more contemporary terms - one could consider particular kata as the preferred 'sports specific strength and conditioning regime' of an art. The fact that they're done over and over could be an aspect of 'learning the drills' and/or 'remembering the plays', too - none of which mitigates the need to actually 'play the game' (randori).
Ergo, randori is the application of these developed attributes. Without it, you're doing a quaint style of Taebo
Case in point:
Take a look at (for example) this fairly odd looking kata. If you've ever done karate, it may ring a bell
then consider it in light of this
I happen to like Matt's ideas, teaching method (3-I) and arguments. He makes a compelling, logical and well reasoned argument - for randori. But martial arts > just randori. (I'm open to the obvious counter argument, too. As always - ICBW).
PS: It should be pointed out that certain arts use kata as two man 'drills' - and against resistance, to boot. An example would be Judo's katame-no-kata. In fairness, judo is a bit of an outlier when it comes to it's kata practice.
In the end, I don't think there's much conflict between kata and aliveness, except when folks try to 'fight with deadlifts and bench presses'. Further, none of this excuses martial arts as shallow practice, social / cultural dojo issues etc YMMV
PPS: IIRC, In 'Judo Formal techniques', Otaki & Draeger break the 'ideal' mix down as 17% Kata, 80% Randori and 3% shiai (competition fighting). (The exact numbers may be wrong, so please check yourselves). Always though that was pretty interesting...