We said if they chose to live at home we would still suggest living in halls for first year for the "experience" of it, making friends, being able to join in impromptu kitchen conversations at 11pm and last second arrangements on the whatsapp group chat for either the flat or the course etc. Then it was up to them if they wanted to continue to live out or at home.
I think several things play into it. The ease and cost of the commute, the friendships they may already have, the personality of your child. My sister lived at home whilst I was away at uni and had a great time, always out, crashing at different places but she also had a boyfriend who worked and a group of friends who didn't go to uni. She had had a gap year working, kept the job whilst at uni.
Her son also stayed home but was a complete homebody and literally went to lectures and came home, never stayed out, never tried to meet up with other people. Was he happy? Absolutely, he loved it, this was fine for him but he is a completely different personality to my sister who is larger than life. My sister feels like he missed out even though they both lived at home for uni.
You can always go to uni and live in your room too, not go to lectures as lots are online, not join societies, not venture out very much. Accommodation costs can be a driving factor and rightly so. Ds has just finished his first year and was looking at what he could rent on Rightmove local to home for the same price. He was shocked by it.