The supply limit is irrelevant in this case. In order to remain secure, the cost to attack Bitcoin must be proportional to the value represented by Bitcoin. Currently, when proof of work is performed, it is funded in large part by increasing a ledger value without a corresponding decrease elsewhere (aka "minting"). In the future, when proof of work is performed, transaction fees will need to increase in order to provide a similar incentive.

If the sum of the block reward and the transaction fees decreases, then that would result in fewer groups willing to perform proof of work calculations, and would be followed by a decrease in the proof of work difficulty in order to maintain ~1 block every ten minutes. That lowered difficulty then results in a lower cost to attack Bitcoin.

So, there must always, always be profit in running proof of work calculations. Not only that, but to maintain the security of the ledger, any increase in Bitcoin valuation must result in a proportional increase in proof of work expenditure across the entire network. It's an absolute disaster of a system.

Transaction fees will dominate the block subsidy long before that. Probably within the next 2 decades (in which the subsidy drops 32x).