If we imagine a state where there are always three times as many pending transactions as can be processed, it seems clear to me that most of these will not be in the next block under any gas model.
But under EIP 1559 such a situation is impossible. In the long run, you cannot have more than 50% of blocks that are full, because if more than 50% of blocks are full then on average the basefee will be increasing, so it will keep increasing until blocks stop being full. And that’s a pathological case where the blocks that are not full are completely empty; if we OTOH model transactions as a Poisson distribution, then only ~13% of blocks would be full (and if we set max = target * 3 instead of max = target * 2, that drops to ~5%).
Instead, my impression is that eip 1559 trades market efficiency for price consistency
Strongly disagree! As I argue in my original paper, EIP 1559 improves market efficiency by increasing price consistency because prices being more consistent than the supply-consistency-maximizing model (ie. fixed block sizes that are generally full) provide is the efficient thing to do!