If you go during the tourist season, it's very likely full. If you go during early morning or evenings, they are likely to be full as well for people who do daily trips. During day-time, Shinkansen are half-full or even less that that. And I am assuming you had a JR pass, which means you had to seat with the "reservation free seats" which are usually always pretty much full and do not reflect the actual situation of the other wagons.