Satoshi actually had a theory for Bitcoin pricing. He thought it would behave like gold, where over the long run the price converges to the cost of mining it. The cost to run the miners is a floor on the price, because if miners mine unprofitably eventually they go bankrupt.
Miners still receive it from transaction fees, so no. Although the economics of keeping the network secure in the face of no new bitcoin being created and many txns happening in side chains or rollups (or not happening at all) are untested.
Not really. Historically, no global currency since the Byzantine Solidus (whose practical dominance vaned with the Fourth Crusade in 1200-something) has lasted longer than 80-100 years. So, Bitcoin isn't even trying to do so.
That means that the total cost of all the mining divided by the outstanding value of BTC should approximate the floor.
Except when it doesn't. When it becomes unprofitable to mine, all of the miners turn off their machines, and the network dies, it'll go to zero.
Complicating factor is the miners who have free electricity, e.g., setup hooked up to their own solar farm or natgas flare. For them, the cost of mining is the capital investment over their output, so they'd keep their machines running as marginal cost of new energy is essentially zero, but the employees to keep it running? If we're down to very few mining machines running, how quickly does the difficulty scale downwards — fast enough to keep it running?
