Should I really be spending 7-10 out of my 15 days in Tokyo?

I wanted to go to Yakushima Island, so I figured we could just get there while stopping for a few days in a bunch of other cities in between.

so like tokyo 4 days (random day trips to hakone, shinkuku, etc.) –> osaka 4 days(day trips to kyoto, nara) –> 4 days fukuoka (maybe day trip to hiroshima, kyushu, kumamoto) –> Yakushima Island –> 2 days in tokyo.

but someone i know said we should just spend way more time in tokyo than other places cuz theres so much to do in tokyo. im probably stretching myself a bit thin with all the places but its kinda just a rough plan right now.