They are 12 and 9 now. My oldest son has been to Japan 4 times: when he was turning 2, turning 5, and twice last year.
Trains are faster, hence we can cover more distance; and they offer more flexibility, especially when you are on a special-purposed trip like chasing cherry blossom. There are also many special trains in Japan, such as steam locomotives and ones with special themes.
Both my sons did not like baby strollers when they were small, and they never sat on one when we traveled. Sometimes it can be quite inconvenient.