Why is faith more valuable than gold?
He answers the question in what he says in the same passage: it is not perishable.
"That the trial of your faith, being much more precious than of gold that perishes, though it is tried with fire, might be found unto praise and honor and glory at the appearing of Jesus Christ." KJV
Pay attention to the two words: precious and perishes.
In Peter's mind faith ought to be imperishable, and indeed if it is genuine FAITH IS NOT PERISHABLE. It (ought to) endure forever.
The Apostle Paul shares the same view of faith when he said, "Now these three remain: faith hope and love." All that are of material (gold included) sooner than later will disappear, but faith remains forever.
In speaking of Abel's faith, the Apostle Paul goes one step further saying, "By faith Abel still speaks, even though he is dead." Heb 11:4
How can a dead man speak? How can a dead person still believe? But Paul says Abel though he is dead still speaks and he still believes!
In Paul's mind faith survives death. The flip side of this coin is that we are to live by faith "always", that is, beyond the time and space. Faith is not something you believe while you are physically alive and stop. It is not something you stop having as of you breathing your last breath. Faith outlives the time (of life and death). So too you should live by it!
Peter flashes the same view of faith when he says in 1 Peter 1:9, "[...at the appearing of Jesus Christ...] Receiving the end of your faith, the salvation of your souls." The idea here is that your faith if proven genuine outlives the time of your physical 'life' here on earth in a physical body. When you die physically, the functionalities of your body as well as your souls such as the cognition of your mind also cease to operate. Yet there ought to be some other functionalities that enable you to be capable of believing even through and beyond your death bed. What is it? It is the Spirit resting on and in you!
Thus faith that is from God not from man is a spiritual commodity. By the same token, man without the Spirit is without faith, and therefore remains dead.
Man without faith remains condemned to hang on and live by that which is of limited value. In the capitalist society, man without faith lives by relying on money ($$$) such as salary. Faith is faith in Jesus Christ who never changes, so as one loses this faith he lives by fake faith that believes in that which is perishing. As the money or gold he relies on perishes so will he perish.