A lot of these posts don't seem to understand that there are different reasons why a baby might wake and cry in the night.
Of course sometimes they wake and cry because there is something wrong - hunger, teeth, wind etc.
But sometimes they wake simply because they have come to the end of a sleep cycle. All of us come into lighter sleep phases between sleep cycles, and we might wake momentarily. An adult will simply go straight back to sleep (transitioning into the next sleep cycle) and won't register or remember these tiny wakings. However, a baby who has learned that they need to be fed/cuddled/rocked in order to go to sleep will not be able to go straight back to sleep and will instead wake fully. And then they will cry, because they want to be asleep and can't get there by themselves.
This is why parents often find their child wakes at regular intervals in the night - every hour or every 2 hours for example. It's because the sleep cycles are regular lengths, and a baby might wake after every 1 or 2 or 3 cycles.
This is also why many parents find that once their child knows how to self settle (whether taught by CC or not) the night wakings drop dramatically - because when they can self settle, they only wake fully and cry when there is a genuine problem, not just because they have woken and don't know how to get back to sleep.
So teaching a baby to self settle is not the same as teaching them that nobody comes when they have a problem.
By way of example - we used CC to teach DD to self settle. She stopped waking every 90 minutes as she'd previously done. However she still wakes every time she is ill, teething, hungry, too cold, etc.
I should add that some people are very lucky and have a baby who learned very early how to transition from one sleep cycle to the next. (Usually these are the babies who love sleep). Those parents will probably not suffer so much through the 4 month sleep regression. Their child will only wake when genuinely hungry or unwell. For these parents, CC would be pointless. However for those of us whose babies have learned that they need to be fed or cuddled to get back to sleep, CC can be a godsend.
It also seems to me that most newborns can self settle in their first week or so. They drop off anywhere, any time they are tired. Then in their first few weeks, as they get used to going to sleep after a feed, they start to learn that a feed is a necessary part of going to sleep. It's then that the ability to self settle disappears. So it's actually not teaching them to self settle, it's re-teaching them - undoing the feed-to-sleep association that we taught them in the early weeks.