There is no evidence because there is no funding really to study it. It's not that there has been research and it's shown there is no benefit. Unfortunately, much of scientific research of that sort is done by industry (to make a profit). Pharmaceutical and biotech companies have studied the consumption of placentas for other sorts of things, but those are placentas procured from hospitals and sold to others. They can't make millions from selling you your own placenta so they have no interest in investing in the research. It's marginal enough that there is no public research funding for it. I'm a health scientist. I can barely get funding to do my own research and I study HIV/AIDS, so a really important topic that gov'ts usually have a lot of interest in investing in. There have been a few small community surveys, which seem to be positive, but they are still small.
Your best bet is just to talk to people who have done it. I had it done with my first and I'm doing it again with my 2nd. I really do believe it probably saved me from postnatal anxiety. I started to develop really awful and disturbing postnatal anxiety and intrusive thoughts about 5 days pp. It was really upsetting and debilitating. I started to take my placenta capsules right about then and within about two weeks it was completely gone. Would it have gone on its own? I have no idea. Maybe? But I had the money to spend and I'd rather try that first before having to go on antidepressants or anti-anxiety meds. I was grateful to have had the capsules. I also was anaemic after birth (Hb of 6) and I think they surely didn't hurt in bringing my iron levels back up. I was also taking iron tablets and spatone too.
I think if you are struggling financially and you are on the fence, maybe not. If you have the money to spend on it and you feel you'd rather have the reassurance that you have something natural to try in case you do need some extra support, then there is no harm in doing it. I certainly wouldn't be without it after my first experience and I don't know anyone who has tried it and was unhappy with it.