I live in Japan and you absolutely do not need to book trains in advance, ever, for any reason. It's a good idea if you're planning to travel during peak hours on the first and last days of a major holiday period, but there is a free seating area that you can ride. The only downside is that you may need to wait a bit on the platform until you're squeezed onto the shinkansen. You're sacrificing some comfort this way, but it's not a strict need.
But that problem only occurs 3 weeks out of an entire year. Also, the normal free seating tickets don't have a reserved time. They're only limited by day.
And my experiences in Europe are similar. Show up, buy a high speed rail ticket, hop on a train and go to the next city.
I've only ever needed to reserve tickets in two countries: one was dealing with Amtrak in the US, and the other was trying to take a train in China between two cities in the midst of the biggest holiday of the year. Other than that, it's always been a show up, get a ticket, and hop on 5 minutes later sort of deal.