Is a pass worth it for this itinerary?

Konichi wa! I am excited about revisiting Japan in September this year, 30 years after living in Hiroshima for 2 years!
Our anticipated itinerary is below, and I am wondering if a rail pass is worthwhile?
Day 1- arrive Narita, stay central Tokyo
Day2, 3 - Tokyo
Day 4- early train to Kawaguchiko
Day 5- v early departure if possible, to Osaka & on to Wakayama
Day 6-10, buses and hiking Kumano Koda, so no trains

Days 11-15 - to Hiroshima & local buses/ streetcars, visiting friends
Day16- return to Tokyo, night flight out

We can be. but flexible with this, but as you can see, there are multi-day spells with no train use, which, due to geography, we can't time differently! A 14 day pass would start after our arrival date, so wouldn't help us the city but would allow us to cover the trips and the ride back to Tokyo. However, I am wondering if it's worthwhile financially?

I'd appreciate some advice :)

Arigato!