The university course my child wants to do does not require maths. Why should he/she choose a mathematics subject in year 11 or 12?

Just because mathematics is not listed as a pre-requisite does not mean that there is no mathematical content in the degree. Universities are businesses competing for customers, in this case students to enrol with them. Making the entry requirements just a little bit easier makes some courses more appealing or popular than others. Once a student has enrolled though, they will still have to learn the mathematical knowledge and skills. And they will have to learn it at the same time as all the other new ideas in the course, putting themselves under more stress and pressure than if they had first seen it in high school.
Alternatively, students who do not take the appropriate high school subjects will take longer to complete their degree and have to sign up for bridging courses to fill in the gaps. Even if this only adds a single year to their study it is one less year of being employed and earning a salary. The amount of this lost salary is equivalent to what they will be earning just before they retire which is significantly more than whatever they start at.