Do caps deteriorate with time even if an amp is not being used?

I believe it is very dependent on what the amp is and the quality of components that were used. If it is mass-market junk then 10 years may be a big deal. If it is high quality equipment with good components, then 10 years should be nothing.

^^^^^^^^^^^
not an amp but still capacitors

I have a Studer tape machine that failed on me a few years ago. It would power up, but when you spooled up a tape and hit rewind, ........nada.

My tech told me "it’s probably the power supply capacitors. I have them in stock bring it over". As I waited and watched in amazement, if you have ever seen the inside of one of these machines; he checked out the power supply capacitors, and they were showing/testing "like new" . Huge things and I remember Made in West Germany labels.

The new, replacement ones were sitting on the table. So do we switch them out I asked. He said "No, I wouldn’t touch those."

Lack of use and lack of cycling caps are their worst enemies. Particularly if the electrolitycs are of "exotic" type.