In July, it's not a climb or a hike or a nature walk in the sense that you might expect; more a conga-line of wheezing tourists. Probably less crowded on weekdays than at weekends. Several decades ago, I was thrilled to see the dawn from the top of the mountain but I have no desire to do it again.

Putting up a shelter is not permitted. If you want to stay overnight, you need to reserve a place at a hut in advance. Forget about being spontaneous.
Regulation and Rules for Climbing Mt. Fuji | Regulations and Rules | Official Web Site for Mt. Fuji Climbing
https://www.fujimountainguides.com/fujisan-hotel.html

There are hundreds of other mountains in Japan ... Unless the sprog has specifically asked to climb Fuji, I'd be inclined to recommend hiking around Yatsugatake or some other beautiful area. (Yatsugatake is roughly the same region as Fuji - with views of Fuji in the distance. There are other mountain ranges all over Japan).