To be perfectly honest, the nurses in our NICU were way too busy.
They did have volunteers come in to be "baby holders" for those that were healthy enough and the parents couldn't be there a lot. I actually signed permission forms to allow this for my dd
DD was not held very often by these wonderful volunteers but the very few times I came in and she was being held, I really appreciated it (it gave me a few minutes to go pump without guilt!).
There was also a night nurse who loved my dd and she would walk her around the NICU so dd could "look" around, lol.
FWIW, the "baby holder" job was a competitive position! There was a long wait list for those few hours and the volunteers were thoroughly screened. Every person who was not family and had contact with the babies had to have background checks, certified healthy by a doctor, and have several personal references. Plus, as I mentioned, the parents had to sign forms granting permission.