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

Not all capacitors store energy for transients. Those big ones in power supply - yes. They also act as part of filter reducing "ripples" in the DC which remain after AC/DC conversion.

Now, small caps in the amplifier are NOT for power storage. They serve many purposes. For example, isolating one cascade of amplification from another. Capacitor passes AC but not DC. Music is AC (not to be confused with AC mains). Another purpose is to improve stability at high frequencies. Some may not be even part of the amplification and rather operate buttons and such.

conrad-johnson (no caps on the names) have always used very simple circuits and very highly specified parts. Their reliance on film caps, including large value ones is contributes significantly to their product's cost.

The hallmark of a good preamp is how quiet it is. One of the benefits of capacitors is that they help the preamp from introducing noise into your system. 

I am going to hijack a bit here because I have a similar question about DACs.  Take a look at the inside of a Denafrips DAC, they have large arrays of capacitors, what is their purpose in this case? Follow up question, do large arrays of capacitors represent a higher risk of failure or sound degradation given the increase in odds? Not picking on Denafrips BTW, they are just popular and seem to favor this design.

I’m just starting to learn about electric circuits and am fortunate my audio club offered a class including using a meter and oscilloscope . Still trying to figure out what signal generator to buy. Anyway, I’m learning about capacitors here