Depends on the time period, really.
Honestly, I like the current arrangement (which is pretty near to your description). To my understanding, the default is for people to have Shinto ceremonies for birth, for coming-of-age, for marriage, and then have a Buddhist funeral. Shinto is seen as more about life and living, and Buddhism as more about the internal and the beyond.
I'm not Japanese and don't live in Japan though, so take that with a healthy grain of salt.