This isn’t exactly a new idea. What I think is new is trying to work out what sort of conlang has the most medical benefits and would be practical, i.e. not to big, not too hard, not too unlikely to be useful.
Communication by other means.
Helen Keller’s language, sign language and Blissymbols are all kinds of “medical conlangs”, language that are invented to deal with something that at it’s root is a medical situation, such as blindness, deafness, or otherwise being unable to communicate by ordinary means. This is a mostly solved problem. ASL is a real living language. But it is difficult as a real language, so a simplified signing conlang could be a way to start signing without dedicating the years of study it takes to get good at a real living language like ASL.
Communication with Babies and pre-speech infants. Not necessarily as an effort to create super babies, but merely as a recognition that language understanding happens before babies, infants and toddlers can wrap their tongues around their language’s phonemes. Already, some parents teach their toddlers a subset of ASL so that children can communicate basic things like, “My teeth hurt”, “Change the channel or I’m going to cry”, or what ever it is that they are really saying. At the doctor’s office, infants and toddlers can’t report on their symptoms, so toddlers are much more likely to have their medical problems misdiagnosed. If it only takes 30 or so hours to get a adult some basic competency in toki pona, then toddlers probably could pick up a signed version even faster than that.
Alzheimer prevention and mitigation. Bilingual speakers get alizheimer’s later. If you don’t need to be bilingual for organic reasons, such as for a job, then a conlang may be an easier way to get that second language in your mind.
Stroke mitigation. Strokes sometimes spare one language over another. A small conlang might be more time effective insurance than learning a complete, rather hard natural language.
Depression. Cognitive therapy, is trendy at the moment. A conlang could be designed to grammaticalize some of the recommended analysis that patients are supposed to do for their inner dialog. For example, people who are depressed tend to under estimate the positive things they can expect from a plan, in part because you don’t have to put it into words. A typical cognitive therapy exercise asks patients to write down their expectations and then see if their expectations matched actual results. If the language required you to include evaluations of expectations in order to create a verb, then one would get very good at making evaluations and it would be more difficult to quietly expect the worst of everything.