For now, that's true, since miners are mostly paid with newly minted BTC. The payout for the job of mining is currently based on BTC's valuation, but the reason for the mining is to secure the transactions. That also aligns with its design.

Why else would Satoshi design Bitcoin's block reward to slowly dwindle towards zero? Apparently in his vision, the eventual steady state for Bitcoin is to be supported entirely by demand for block space (aka, transaction volume), with no correlation to "value in network".

Edit: to put a finer point on my question...

Does the transaction-fee-only mining model work?

If it does work, isn't the current block reward wasteful, funding tens of millions of dollars a day worth of mining, when the fees set by competitive demand for block space are a fraction of that? If fees alone are going to be enough to secure the network adequately, why can't Bitcoin adopt a more aggressive halving cycle and move to fee-only by, say, 2040 instead of 2140?

If it doesn't work, that means there will eventually be a problem with Bitcoin as it slowly moves toward that model. How can Bitcoin change its design to fix this, without compromising the "only 21M coins ever" promise that many of its stakeholders consider a fundamental strength?