8d7n in Japan

Hi, I'll be travelling to Japan with my family and there will be a total of 5 of us. Since there will be 5 of us, it will be more difficult for us to get around in taxis so we'll be travelling via train most of the time.

I'm wondering if it is worth it to purchase the JRpass and since we will be there for 8 days and I was thinking of purchasing the Haruka pass on day 1 to get to our accommodation and active the JRpass on our 2nd day so that it will last till the 8th day.

This is my itinerary.
Day1 & 2 - KIX Airport -> Osaka
Day 3 - Osaka -> Nara -> Osaka
Day 4 - Osaka -> Kobe -> Osaka
Day 5 & 6 - Osaka -> Kyoto (we'll be staying in Kyoto for 2 days)
Day 7 - Kyoto -> Osaka
Day 8 - Osaka -> KIX Airport

Please advice. Thank you.