The problem is that if you stop increasing the supply, then you're relying entirely on transaction fees to reward miners.

But transaction fees are determined based on supply and demand for transactions, not based on how much value on the chain is secured by them.

These are only tangentially related, and the strategy of 'store of value' makes them even less well coupled.

Unless there is high demand for transacting, then the economic pressure will be for the cost of attacking the chain to come down, and double spending the value stored on the chain will increasingly become more appealing than transaction fees.

The current equilibrium relies on the supply increasing.