The rules may allow the child to sit in an empty seat. But you're more likely to be asked to vacate that seat. The culture is a little different.
In the UK, reserved and unreserved seats are in the same carriage - and if someone finds another passenger occupying their reserved seat, the person with the reservation may often just take an unreserved seat. (IME, asking someone in the UK to vacate the seat that you have reserved can elicit foulmouthed protests ... ). In Japan, carriages are designated as "reserved seating" or "unreserved," and a person who has reserved a seat will expect to sit in it. If they just move to another seat nearby, there's a good chance they'll be asked to move by the person who reserved that seat.