Today, I was reading more about the market impact theories in the economy, and not only they define the permanent price impact which is the same as our discussion here (affects the current transaction and the ones after that), but also they introduce a temporary price impact which translates to affecting only the current block and not the next ones! Moreover, even there are theories of elastic markets in which the magnitude of temporary price impact dominates permanent price impact which is quite the opposite of EIP-1559. BTW, I have not found anything in which there is zero market impact for the transaction itself.
This brings me to suggest that we can still use EIP-1559 for the temporary price impact if we want to have a multiplicative formula that is supposedly more responsive, but for the permanent price impact, it is absolutely necessary to consider a path-independent update rule! Moreover, we can have an exponential path-independent dynamic pricing formula that is super responsive. For a thorough comparison from the economic literature, see here.