No. They are not flawed.
Exactly, the incentive model works well. And it will continue to do so even if...
the block subsidy is very low versus the value of the fees and the value of BTC is high
.
You are right that there must be a certain "average transaction fee level" per block (which you mention as g(x) ) to maintain the security of the chain when block rewards continue to descend. But your conclusion...
the block size will have an impact on how secure the chain is.
is flawed. The
amount of transaction fees and
maximum block size are not directly related, and their relation is pretty complex.
In late 2017, for example, Bitcoin had less block capacity than now because the percentage of Segwit transactions (which have less weight) was lower, but transaction fees were much higher than now, because blocks were fuller - that means, people were panicking to get their transactions included, and thus offered to pay high fees.
If the transaction block limit is too high, then - as was already written by others in this thread - the average fees per transaction stay low. In BCH, in theory I can send transactions for the absolute minimum because blocks are almost never full.
Now imagine the block size limit stays low at 4MB, and most transactions are carried out on sidechains, the Lightning Network, and other off-chain mechanisms (even centralized ones, like via Coinbase). The transaction fees on these "second layers" would be low, but their "wellbeing" depends on transactions on the main chain (be it via atomic swaps from and to sidechains, or channel opening/settlement transactions on LN). So in a world with high Bitcoin adoption the second layers would provide enough demand to ensure the transaction fees on the base layer stay high enough.
I agree however that at some point in the future block size should be increased, but this is not a priority issue now. Schnorr signatures and friends are much more promising in the near future. It would become a priority if the working of second layers cannot be ensured anymore with the current block size, e.g. if the demand for LN channel opening/settlement transactions is as high (or almost as high) as the block capacity.