This indeed can be requested. It may not be granted in all cases, but it can be done when requested specifically. And this is an example of applying specificity to good advantage rather than take one’s chances in what the divine will do on the way to healing something. As you know, and as is stated in the question itself, symptoms of a malady are often the very last things to change, and that is a deliberate arrangement to keep the heat on, so to speak, to keep the pressure on the sufferer to keep working on their issues and take seriously the karmic message being sent them in the form of an infirmity in the body that has developed. Without that incentive, people will not have any other way of being reminded something is still not in alignment they must take care of, because it is an obligation to the universe. So those very disease symptoms serve as a constant nagging reminder of unfinished business. But this is not to say they cannot be muted in a way that makes life more tolerable and less acutely painful.
And we agree, in the majority of cases having recognizable and somewhat disturbing symptoms is enough to provide a warning and incentive for people to explore what might be happening and find answers, short of a malady becoming incapacitating for all practical purposes if people are so impaired they cannot function reliably and be gainfully employed, for example. There are many on the sidelines whose lives are worsened and become ultimately unworkable because they are so dragged down by illness that they become more vulnerable than can be survived. There are karmic circumstances that call for an earlier death than would otherwise happen, but that is not true for all. So, much can be gained by asking for relief along the way to having a full and complete rebalancing of the underlying karma, and this will help many individuals to have a way of coping more effectively than in the absence of this workaround.