I would say that following a routine, absolutely does not equate to leaving a baby to cry for hours, which is clearly what many people (understandably) object to. It seems to be a common misconception, that following a routine, with one of the aims being to help baby sleep longer, must require long bouts of crying. This is not so.
I have never used controlled crying. The only people I know who have done that, have done it with children well over a year and then in desperation, because their children have been waking many times in the night and wanting milk every time and because they had poor sleep associations. So actually, the people who often resort to controlled crying are actually those who have never used a routine, not those who have. By using routines from an earlyish stage, babies don't need to do controlled crying. They wake in the night when young,of course. Their daily routine of feeding and sleep is what allows them to gradually go longer in the night. When they cry in the night, it is for food and the mother or parent goes to them and feeds them. There is no suggestion of leaving a small baby to cry in the night for food. As they get bigger (heavier...returning to the original question in the thread, which the OP was interested in) they can eat a bit more in the day and this, with carefully structured sleep between 7 and 10.30 allows them to gradually sleep longer. Typically, such a baby, after 6 weeks will wake just once between 11.30 and 7. Initially it might be around 2am, but gradually get later, as they are bigger and eat more at their feeds. Eventually they sleep until perhaps 6 or even 7 and that longer stretch has been achieved, probably by around 6 months.And without lots of crying.
So, yes it does benefit the parent. And I dont think it has been achieved through leaving a baby to cry. And yes, it has benefitted the baby, because there is never any later possible need to try and break negative sleep associations. I think that most people with children who wake frequently in the night beyond about 3 or 4 have various attempts to break that cycle....and these are not easy for either parent or child. Of course, many children may just naturally sleep through from 18 months or 2 years or whenever. Fine, if you are happy to hope yours will do that and to wait until then or later if they don't.
So please don't say those using routines leave their babies to cry. That is not the idea at all. Yes, the routines benefit the parents, but the babies are certainly not harmed, as some posters are suggesting. Controlled crying as a method would never be used on small babies, and those on routines don't need it because they sleep before that point.
Again, it is parental choice about approach. People can choose to intervene and guide their baby towards sleep, or be totally baby led if they wish. Neither is wrong or cruel. The 2 approaches might have different outcomes in terms of babies sleep (which is fine, as long as parents understand the likely outcomes) but are equally valid choices.