yes there are many criticisms against psychiatry that are valid, but these are mostly criticisms of the medical model in general. more psychiatry doesn't mean more suicide (except perhaps the evidence that short hospitalizations increase suicide rates) nothing we do one way or the other affects suicide rates on the population level. see
here for a more realistic criticism of the problems with psychiatry and residency training.
Have a look at UW, Hopkins, UMN, maryland, yale, as programs that often have specific PGY-2 spots that are generally for people transferring from other specialties. And just inquire anywhere you're interested in.
I have never seen an applicant who didn't have a psych letter so I would strongly suggest one even if you have barely known them. People transferring from other programs often have a letter "yeah I know this guy, we like him and think he would good" and leave at that, and they still match at top programs. Try and do an elective, or attend psych meetings/grand rounds, observe rounds etc. But I would just go ahead any apply without it and send in the letter as soon as you can. don't waste anytime.
If you are perturbed by people riling against the specialty, you won't last very long. Yes there are many, many people who are critical of psychiatry with good reason. But part of that is because there are alot of angry people with mental illness who displace some of that onto psychiatry, who re-experienced abuses within treatment, because psychiatry is an easy target for criticism, and because it has greater visibility. No one complains about radiology because they don't know what it is or what radiologists do. There are people who are anti-medicine, peds, obstetrics, surgery, vaccination etc etc. There is still a growing demand for psychiatrists because so few psychiatrists wish to work with the mentally ill and are so geographically unevenly distributed. No one wants to do the work of psychiatrists (working with high risk patients with complex medical, psychiatric and substance use comorbidities), not psychologists, not NPs, not PAs. We're not going anywhere.