There is a lot of research it seems on both sides. What you generally find though is a short study or small sample size which makes neither terribly compelling. I haven't yet seen anything that fits both criteria, meaning longitudinal and large sample sizes.
Since I personally couldn't find enough of anything in research to decide what is best I trusted myself to think it out & I can explain how I came to my own conclusions, but they are literally my own rationale, as again, I didn't find any study to be thorough.
When my kids were small I breastfed. When they cried my body reacted through letdown & this continued well into a year of age. So for me leaving them to cry for the sake of crying wasn't going to happen, as I trusted my biology was designed that way for a reason & the feelings it was triggering within me were meant to be paid attention to.
In general too I am not a big believer in "crying for no reason". I am not. Crying is all a non verbal child has to communicate being unhappy. So I may not know why a baby is unhappy, but I am not confused on whether they are happy or not when I hear crying. I do not want my children falling asleep unhappy if I can help it. I prefer them to have a peaceful, good feeling about sleep. So I work on ways to help them learn, over time, to go to sleep without any tears. I won't lie & act like they were sleeping through as tiny babies. They weren't. That isn't fun to be that tired, but it's also not the worst thing ever, so I rode it out. What I think I did get in the end, was that by age 2 all of my children went to their beds without any fuss, no push back, no tears, no trying to run off. They have all seen bed as a positive thing overall & even though they are older now & might ask for more time, particularly on a weekend, they also don't give me flack if I say they have to go now.
While I understand that those that leave infants to "self soothe" feel that the child is learning to self soothe, I just don't believe it. When I am upset I call a sibling, talk to my spouse, a friend, someone. I reach out. I don't soothe myself when upset unless I have absolutely no choice & every therapist out there would suggest I should not be self soothing all the time, that reaching out & connecting is actually the healthiest way to navigate hard times. The last thing I want to teach my children from early on is to turn inward for soothing. The concern I have is the massive numbers of young people today, that when upset, instead of turning to parents & talking about it, use things like bulemia, drugs & alcohol, self harm & other measures to cope. That is concerning to me. I want from the very start of my children's lives for them to know, you never ever have to deal with upset alone, not little upset, not big upset. You always have me. I may not be able to change it...bedtime is bedtime, but I don't have to leave you alone to get through it. People constantly mistake tender, engaged, connected parenting as permissive. It's far from it, if in fact you are engaged & connected. Allowing my children to know I care about their feelings isn't the same as allowing them to do whatever they want. In fact in early years, most of their upset is all about decisions I have made, like we cannot go outside in the pouring rain when it's cold. I can still take the time to listen to my 2 yr old try to tell me how angry it makes him that we can't play outside. I can tell him I am bummed too. We can discuss how much we hate rainy days like this. None of that is permitting anything other than a bond. I think of sleep & babies no differently. I want them to know that if they'd rather not be alone, that is okay. You don't have to be & I won't make you accept that. You can be alone to sleep when you feel ready to do that & I have faith you will some day. The funniest thing to me is that my husband & I slept separately for a very long time with one of our children, because she couldn't sleep alone well and he got calls at odd hours that woke her & it was a mess to try to all be together. And grown men would act all like they felt sorry for him sleeping alone. Can you imagine? My poor husband sleeping alone, scared of the dark? I mean for real. No one feels sorry for the baby alone, but feeling sorry for my husband temporarily sleeping alone because the men don't like sleeping alone, imagine that. They don't like it, but they think an infant should. Even he found it hilarious. He feels the same way I do about sleep & our kids & it's never bothered him one bit.
Unfortunately on this particular subject, you can find a study to back any position you take on it. They all exist. I chose to trust that it didn't feel like letting a child cry lined up with human biology & development, so I opted not to take that path.