Yes loads of parents do! But in my experience, less do it with their first child.
I too couldn't do it with my first child, couldn't bear to hear him cry for 1 minute. So co-slept, breast fed and rocked etc etc. I was sooooooooooo tired for the first two years.
However, when I had my second baby- it was important to me that I still had time to read a story and snuggle DC1 at bedtime.
So DC2 was left to cry for short periods, so I could put the older child to bed. Sometimes baby was already asleep and I was bathing DC1. But then baby would wake up. I would have to get DC1 out of bath, put towel around them etc. I went at a calm pace, didn't race up to baby - because what about DC1? Surely it would have been cruel to neglect older child's needs.
Parenthood is a very long game, if you can't leave them to cry - don't - maybe you might with your second or third child? Maybe not?
But honestly, don't fret over it. It's just another choice - like going back to work, or not? Breast feeding or bottle? Giving treats or not? The list goes on and on and never stops - always this battle between philosophies and ideals. Your baby is in your family - where you make the rules. And if your family gets bigger you may inadvertently have to let the baby cry.
Just do what works for you and your family.
You can still be the most wonderful, patient and loving parent and do some form of sleep training. It may work - but it might not.