You're only half right. Belief on the part of all users is a big component. But the other part is the strength of the protocol and network holding it all together. The Bitcoin network itself does have intrinsic value, and reinforces the belief part. They rely on, depend on and reinforce each other.

But the price alone does not dictate a crypto's value. Anyone, literally anyone, can create a crypto and pump it to the moon with enough money. I.E., create a crypto with a high number of pre-mined units, release only a tiny, controlled float onto an exchange, and buy it back from themselves. Voila, instantly high market cap! This is the literal definition of a penny stock pump and dump.