Why have capacitors improved so much over the years?

I can't understand either why manufacturers go through all the trouble of designing a piece of gear & then at the most critical point insert cheap caps.

When design engineers select components/parts for their circuitry, it is their responsibility to assure all components/parts are up to required specification and not to compromise safety and reliability.
Most boutique audiophile capacitor manufacturer cannot provide required documentation for design engineers to consider installing such capacitors in the design.

@widmerpool Absolutely correct.  Even table salt versus Kosher salt.  And even among brands of salt with Diamond Kosher salt generally superior to other brands.

My EAR 890 amp uses cheap electrolytics, downrated from the original build and then, after they started blowing amps, uprated in the current version.  This is an abberation of EAR equipment.  I haven't had a problem and understand that Paravacini designed his equipment to a price point.  He didn't use the top quality parts but he chose parts which would work and produce the sound he sought.   His genius is that he could take more conventional parts and design great sounding equipment at a price point, not cheap but not high end expensive either (besides his commercial product work).  His affordable tube phono preamps are still highly regarded at their price.

Good post @fleschler. Tim's U.S.A. doppelganger was Roger Modjeski of Music Reference and RAM Tubes. Roger argued that the use of costly boutique parts was often unnecessary, as their claimed superior involved matters unrelated to the part's function in a particular circuit application, and therefore provided no sonic benefit. He further argued that some boutique parts actually compromise a circuit's behavior, leading to not just inferior sound quality, but in some cases reliability problems. Music Reference products are known for their superior stability and reliability.

And a second on Paravini's EAR tube pre-amps: After auditioning the EAR 912 pre-amp, Art Dudley stated in his Stereophile review that it was the first pre-amp he had heard which challenged the sound of his Shindo. The 912 was out of his reach (mine too ;-), but the excellent 868 is an over-looked nice little pre. Single-ended and true balanced outputs (two stereo pair of each, the latter via Tim's world-famous transformers), able to drive a 200 ohm load!

Roger argued that the use of costly boutique parts was often unnecessary, as their claimed superior involved matters unrelated to the part’s function in a particular circuit application, and therefore provided no sonic benefit.

I totally buy this. A great deal of this is driven by armchair buyers who will nit pick relative quality and value based on parts instead of performance.

Of course, a large part of it is manufacturers attempting to make gear to sell specifically in the high end.  What if the best sounding amp on earth cost $100 to make?  No one would buy it, unless it had meters.  Big, beautiful bouncing meters.