Hello AlexS
Welcome to the SBB Community.
The truth of the story is explained in one sentence: for children holding the Swiss Family Card you do not have to purchase tickets, as they travel for free with their parents when they hold for themselves a valid ticket.
Why should you purchase a CHF 0 ticket? We Swiss like it efficient, we do not make ourselves extra work when it is not required. So easy, right? 🙂
And yes, since our trains are free seating (except of GEX, GPX, and GOPEX trains), a seat reservation is also not required and tickets do not come with seat assignments.
Google certainly would have directed you towards our SBB Community, your question is a frequent one, at least two times a week.
Kind regards,
Roland