Not all fares work for all passengers; if you require guaranteed seating together, book main cabin, and consider it just part of raising your children. You being allowed seats together on a Basic fare is like me asking the IRS why I don't get a child tax credit.

Remember that if you "chance it" and the gate agent decides to be nice to you, it's a good chance the person displaced paid main cabin rates specifically to select a seat, and that's not fair to them.