Is 7 day pass worthwhile for our trip?

Hi there,

We are spending 10 days in Japan. On the third day, we are leaving our hotel in Ginza for one night at a ryokan in Hakone. We are then going from Hakone to Kyoto and Kyoto to Tokyo before spending our final three nights in Shinjuku.

Given where we are staying, does the 7 day pass make sense? I looked at the Romance Car but the observation deck tickets are already booked. I was still thinking it may be more picturesque, but it looks like we will need to transfer on the Hakone Tozan railway to Kowakidani in either case This would also let us take the Nozomi from Kyoto to Shimbashi.

I guess the benefit of the 7 day pass is 1) it would be maybe 3-5k jpy cheaper, 2) the Shinkansen stations would be a little closer to Ginza, and 3) we could just hop on the train without worrying about having to book at the station.

Any input on logistics or thoughts would be greatly appreciated!