I don't think I necessarily agree with your point about it being difficult. Many fields are difficult and yes it's tough talking with people who have a mental illness. But I would say most students at my school really enjoyed their psych rotation. And I think there's a serious overestimation of the 'personality' one should have in order to pursue psych. All you really need are patience, compassion, and understanding towards patients, something I would hope all soon to be doctors have. I don't think there's any secret about psych being out but more about people really considering what kind of life they want in the future. I suspect many individuals liked psych a lot but didn't want to go into it because of the stigma/lower pay. The tide is shifting a little as people are making lifestyle a very important part of their decision-making. So while I don't expect psych to become super popular, it will continue to become more and more competitive.
I don't think the "turn off" necessarily is how much you need to like patients.
The big divide you see between cutters vs the not cutters, and then looking at the not cutters as a group, has to do with how important it is to either see results fast, or be able to *measure* results, and how much you like managing *chronic* illness.
Sure, inpt psych you can see come quick results.
Both family practitioners/IM and psychs need to be OK managing chronic illness, however, I would argue PCPs get a higher proportion of one and done type problems in their daily practice. The PNA admit, the UTI outpt.
Outpt psych, usually if it's the situational depression or mild GAD that was gonna respond to a simple course of SSRIs, that never would have made it past the PCP to your door. So often with outpt psych you're gonna have a lot less "cure" to what you're doing. Even if you're just doing 15 min visits for med management, I would argue there's a different quality to the "good" you're doing.
Take CHF, there's a chronic illness, however think of the way CHF is staged. You can actually measure your management in treating with pounds of water weight, SOB/how far the patient can walk, and kidney function. I know psych has all those little questionnaries patients can fill out, but I would argue more than most fields, even ones that manage chronic illness, it is much more difficult to quantify your work. This, to me, distinguishes psychiatrists, neurologists, and palliative care physicians from all the rest in terms of "personality type." A sizeable portion of your practice can have a much less "measurable" feel to the work you're doing, which by no way makes your outcomes less tangible or important.
So, long story short, I think what makes dealing with psych patients "require" a certain personality is that the docs that like it, need to be OK with management of not only frequently chronic conditions, but conditions for which there is much more ambiguity not only in how to treat, but in measuring response. *That* to my mind is unique for the fields I named.
I'll spare you on then getting into what makes psychiatry different than neurology and palliative care despite the simularities I named.
Psych and EM are 'becoming more competitive at faster rate than most other fields' (to borrow your words). If you're a US MD student from a low tier school like me and you don't do well in step1 (<225), you better also apply to some preliminary surgery spots so you won't go unmatched. I kind of regret not taking my DO acceptance now since DO also have their own residency.
My understanding is that there will be a complete merge for osteopathic and allopathic residency programs, although it's expected for each to still maintain preferences towards their own.