I’m more inclined to identify the problem as being that the maximality rule gives probability functions of that kind too much of a say when it comes to determining permissibility.
Another response could be to just look for more structure in our credences we’ve failed to capture. Say we have a bunch of probability functions according to which AMF is bad and a bunch according to which AMF is good, but we nonetheless think AMF is good. Why would we think AMF is good anyway? If we’re epistemically rational, it would presumably be because we doubt the functions according to which it is bad more than we do the ones according to which it is good. So, we’ve actually failed to adequately capture our credences and their structure with these probability functions as they are.
One way to represent this is to have another probability function to mix all of those probability functions (“(precise) higher-order probabilities to the various “admissible probability functions”), reducing to precise credences, in such a way that AMF turns out to look good, like @Richard Y Chappell suggests in reply here. Another, still permitting imprecise credences, is to have multiple such mixing functions of probability functions, but such that AMF still looks good on each mixing function. If you’re sympathetic to imprecise credences in the first place (like I am), the latter seems like a pretty good solution.
Of course, an alternative explanation could be that we aren’t actually justified in thinking AMF is good. We should be careful in how we pick these higher-order probabilities to avoid motivated reasoning. In picking these higher-order probabilities, we should remain open to the possibility that AMF is not actually robustly good.
Another response could be to just look for more structure in our credences we’ve failed to capture. Say we have a bunch of probability functions according to which AMF is bad and a bunch according to which AMF is good, but we nonetheless think AMF is good. Why would we think AMF is good anyway? If we’re epistemically rational, it would presumably be because we doubt the functions according to which it is bad more than we do the ones according to which it is good. So, we’ve actually failed to adequately capture our credences and their structure with these probability functions as they are.
One way to represent this is to have another probability function to mix all of those probability functions (“(precise) higher-order probabilities to the various “admissible probability functions”), reducing to precise credences, in such a way that AMF turns out to look good, like @Richard Y Chappell suggests in reply here. Another, still permitting imprecise credences, is to have multiple such mixing functions of probability functions, but such that AMF still looks good on each mixing function. If you’re sympathetic to imprecise credences in the first place (like I am), the latter seems like a pretty good solution.
Of course, an alternative explanation could be that we aren’t actually justified in thinking AMF is good. We should be careful in how we pick these higher-order probabilities to avoid motivated reasoning. In picking these higher-order probabilities, we should remain open to the possibility that AMF is not actually robustly good.