What's the value in lots of capacitors inside a line stage preamp?

well you have a full life in front of ya.

start pulling them out one by one and see what happens.

In a tube cap some of the most important caps are the coupling caps.  They block DC but allow the signal to go through.  Because all the signal goes through it their character can be the character of the preamp.

Second are power supply caps.  The higher the value, the lower ESR, and L the better they filter power supply noise.

CJ don’t use (smaller) electrolytic capacitors, hence all the film caps necessary for the required capacitance.

@noromance is also right.

I looked at a pic of the inside, and even going back to the PV10, CJ uses capacitors which are just enormous.  Film caps are larger than electrolytic but even among film capacitors there's large and then there's huge. 

Generally, a film cap's size has to do with the uF (microfarads) and the voltage rating.  It looks like CJ is using exotic film caps which for a given uF and voltage are unusually large.  Caps of Unusual Size.  COUS.  (Princess Bride Reference). 

It's also true, IMHO, that for tube preamps the capacitors are often THE sound of the preamp, so it's no wonder for me that CJ is going with exotics.