This would definitely penalize a block proposer who uses a lot of gas by charging him a higher price per gas, in contrast to EIP-1559. But it is still the case that the subsequent block proposer faces an even higher price, as he does in EIP-1559.
A spillover of higher gas price into subsequent blocks may be something that we actually want. There are two reasons I can think of. First, it could be because there is an additional cost from having multiple large blocks occur in a short time interval, holding constant the long run average block size. I do not have a good idea about how large this cost is.
Another reason we might want a spillover is that we want to very strictly adhere to the target block size, rather than consider a cost of overshooting the target and optimizing between this cost and providing additional block space. I personally think optimization could be better if we set the right parameters. But even if we were to choose to adhere to the target, keeping the hard cap of 12.5M gas may be better than allowing a flexible block size and misaligning incentives.
Suppose we find that we indeed want a spillover. Even in that case, I think the mechanism should be such that the proposer of the original block faces the highest price, and the price gradually decreases if subsequent blocks hit the target size. This makes sense especially if the rationale for spillover is that we care about large adjacent blocks. If you are farther away from the congestion, your transactions add less to the congestion, so you should pay a lower tax.