Does it make sense to get a JR pass?

Hello! I am leaving for an impromptu trip for Japan in 3 days and didn't have too much time to plan! I am struggling to decide if I should get a JR pass, not only for cost but for convenience (which is worth a lot to me). This is the itinerary:

April 6: Arrive in Tokyo Narita airport (staying in Shinjuku, Tokyo)
April 7-10: Tokyo (intercity travel)
April 11: Day trip from Tokyo to Shirakawa-go,
and then from Shirakawa-go to Osaka
April 12: Osaka (intercity travel)
April 13: Osaka to Koyasan
April 14: Koyasan to Kyoto
April 15: Kyoto (intercity travel)
April 16: Kyoto to Nara (roundtrip-day trip)
April 20: Kyoto to Tokyo, Narita airport

I know that the 7 day pass is worth it for the total cost of trips, but because the large cost trips are spread out it kind of messes it up. My question is whether a JR pass is still worth it for a period of 7 days SOMEWHERE in this itinerary, and even if it's just shy of being worth it in cost, i'm wondering if it would be worth it in convenience?

Thank you in advance for ANY help!