If you are not catching your Shinkansen during peak hours (between 7 am and 9 am and 6 pm-8 pm), and during bank holidays, you do not need to book your seat and you can use any non-reserved seat by showing your Japan Rail Pass.
In fact, the Shinkansen trains run very frequently (every 30 min), particularly on the Tokaido line, between Tokyo and Kyoto, so you don’t have to worry about booking.
Starting from May 2020, a seat reservation near the luggage area
will be required in the Tokaido
, Sanyo and Kyushu lines if the sum of the dimensions of your luggage exceeds 160 cm