You may expect a situation in Japan to use both flight and shinkansen, but such use is rare for Japanese locals. Flight or Shinkansen + local train (or rent a car) is used in most cases, not both.

For a overseas tourist arriving by flight, anyway it's better to avoid the three weeks. I believe it's on May, August, and end of the year, but former two is Japanese local holidays so you can easily avoid. Then you don't always need reservation shinkansen because free sheets are available (but YMMV).