It most certainly depends on the kid and the family. In our situation, our child wanted to leave home and go to a college 500+ miles away. She wanted to explore a new town, learn to live on her own, experience different weather, solve her own problems, etc. In the end, the local school offered a significant financial package along with other academic opportunities that the school 500+ miles away didn’t.
We had long conversations about how much money a social fit was worth. She chose the financial fit and we agreed to do what we could to help her feel like she was “going away” to college. To this day, she acknowledges the financial benefit but still wishes she would have gone to the other school.
To clarify, our home is always open to our kids. Their bedrooms are intact and we haven’t converted their rooms into gyms, offices, craft or guest rooms. In our situation we realized that her homesickness was about missing family members and not about sleeping in her childhood bed.
Colleges have family weekends, 6-8 weeks after school starts because it is just around the time that students start to feel homesick. They realize that bringing the family to visit the students is healthier for the student’s adjustment than it is for the students to go home.