I can only offer anecdotal evidence but I have worked in private nurseries. I worked for a year in one and for a couple of years as supply around various nurseries. I wouldn't send my own child to a private nursery under the age of 3. Some childcare workers are lovely (obviously I was one of the lovely ones 😆) but a lot are not. It is an underpaid job that too many people go in for because they leave school with not very good GCSEs and don't know what else to do at college. At the nursery I worked at for a year we got a lot of students. And with the very odd exception they were all totally lacking in common sense and any real ability to meaningfully interact with children. Yet they all passed their placements because the bar to pass was extremely low.
I worked in the preschool room in my year long job so didn't get much opportunity to cuddle babies, but if I was ever sent to the baby rooms for staffing reasons the staff were generally sitting chatting and the babies were left to entertain themselves. I used to get told off for picking them up if they started crying as 'they just want their own way.' No, they wanted a bit of attention and love which was severely lacking from the other staff.
In my time as supply I regularly picked up crying children or spent time settling new starters and would be told, just leave them, they just whinge all day. On one occasion it was treated as a bit of a 'miracle' that twin boys in their first week at a nursery hadn't spent the whole day crying, as the rest of the week they had, but that was because I spent that day playing with them and talking to them and generally distracting them from being sad - nobody else could be bothered with that. At another place a toddler was crying and wanted her key worker to pick her up but the key worker refused as the tot was teething and the worker didn't want to get stuck holding her all day. I tried to comfort her but she didn't want me as she didn't know me.
Most toddlers at nurseries quickly learn that if they are playing with something they can't put it down for a second or another toddler will take it off them. They learn to hit and snatch because that gets them the toys they want. Often they don't have to learn to tidy up toys because toys are out all day and staff just tidy up at the end when all the kids are going home at slightly different times.
My mum used to teach primary and as an older, part time teacher if she was ever asked to do a day's supply in the Reception class she always said she could pick out who had been to private nursery the longest. Because they were generally the naughtiest child in the class.
Now, all of this comes from my experience twenty years ago, so hopefully nurseries have changed for the better, but I don't think it's the ideal environment for any child. If parents have to work then if they can find a good childminder I think that's usually a much better experience for a young child. But, in an ideal world, in my opinion, there is nothing better for a 0-3 than being with a loving parent full time.