Dr. Uri Burstyn, aka the Helpful Vancouver Vet, who previously demonstrated several different ways in which to properly pick up a cat, responded to a specific question about carrying a cat like a baby. Using the shoulder-loving Mr. Pirate to demonstrate, the kind doctor responded affirmatively but offered a few cautionary words about safety for both feline and human.
…this is just fine. Now the one caveat I would say that if your cat has back pain they may not appreciate this. You have to be very supportive on the bottom and if your cat has a sore back they may resent this. But aside from that one caveat, to me this is a very good way to carry a cat you trust and a cat that trusts you.