Worth buying JR Pass for 12 days?

My 12 yo and I will be visiting Japan arriving 16 th and leaving 27th April, total 12days. Our flight is to Hiroshima, so we will only travel north, with a rough itinerary of Hiroshima-Osaka-Kyoto-Tokyo, and a couple of day trips in between. My calculation of the cost of single journeys is that they total less than the cost of the 14-day JR pass , and it is cheaper to buy each leg as we go. This also gives us more flexibility as we can take other than JR trains. Please can you advise if you recommend to buy or not buy the JR pass? Thank you.