There is no need to study the attractiveness of someone in relation to an illness they are suffering. It's a completely inconsequential metric that's ableist by design. Additionally, all 3 things you listed can have cures. Starting with the most obvious, many alcoholics are able to reach long-term sobriety, though studying methods to achieve higher success rates is obviously of importance. "Severe mental illness" is incredibly vague. Let's take one example, one that is notoriously difficult to treat: Borderline Personality Disorder (which I even happen to have). You can cure personality disorders, just not with medication. It requires you to spend lots of time in extensive therapy to essentially rewire the way your brain works. A quick search tells me that despite being classically cited as the "most painful mental illness", and one of the hardest to treat, between 50-70% of those with BPD achieve long-term remission from treatment. Given that it's a personality disorder, the definition of "cured" is not exactly clear, but remission brings patients below the requisite number of symptoms in the DSM to constitute diagnosis. Chronic illness is also a vague category, but there's progress being made on cures for many chronic illnesses. For instance, recent developments in Chimeric Antigen Receptors and inverse vaccines bring potential cures to a wide array of autoimmune disorders. These are chronic illnesses that were once thought to be incurable, but we're here sitting on research showing that these cures can work. That is the research we need, not some ableist BS about how people with chronic illness may be less attractive to other people.

As for your assumption about how funding works, there is only a limited amount of funding that goes into scientific research. The less that is wasted, the more opportunity there is for funding going to research that makes a difference.