My two kids are (by choice) day students at different boarding schools. Really it depends on the school and your kid. One of my kids is extremely introverted and is more than happy with his few close friends at school and does not partake in any of the evening or weekend activities. This is his personal choice as he would be welcome at everything the school has to offer. He is still very close to his middle school friends - none of whom are at the same BS - so he prefers to spend his weekends hanging with those kids. I will say that his school does not do as much as it can to integrate the day and boarding kids. Day students are not allowed in the dorms and that is where most of the boarders go to hang out, so they end up in the library during free periods. The school just opened a new student center. That may help things as all kids can go there to hang out during the day.
My other kid, on the other hand, is a little less introverted and has made a ton of good friends - many of whom are boarders, and spends some evenings and weekend days at school doing various activities. In non-covid times, the day students have a “lounge” in the dorms. Therefore, they are truly integrated with all students and can come and go from their lounge or a friends room at any time. She can stay the night and sleep either in the lounge or the room of a friend. Most people cannot tell the difference between a day student and a boarder.
We have offered both the opportunity to become boarders and they both continue to say no. I think there is something to be said for being able to separate school and home, and that really appeals to both of them.
Both kids purposely did not apply to another area BS because it is known to treat day students as 2nd class citizens.
Long story short, it really will depend on the school, how well it integrates its day students and your kid’s personality.