I think such a move would be well intentioned, but it wouldn't be effective and it would actually make things worse.
So, yes, we're entering a future where maths and science are increasingly important, and less and less students are picking it. However, for example, we don't have enough high school students graduating, going to uni to train up to be a maths and/or science teacher, and then entering the education system to make their mark. And of those who are, the number of teachers who can actually teach the content well is very few. Also, of the maths teachers coming through, very very few are actually able to teach 4U maths, for example. Increasingly, I see new teachers coming through who can only teach up to 2U Maths or at most 3U.
So, if you then make maths compulsory, you certainly need more maths teachers. And then increasingly a lot of students will learn maths as a subject in their senior studies, but they will not be taught by a teacher who properly knows their stuff and/or has the ability to teach it. Also, a relevant side effect you obtain by making maths and science compulsory is that you're actually increasing overall student disengagement with the subject. As an example, think back to year 12 students' attitudes towards Advanced English. Furthermore, disengagement is definitely exacerbated when you don't have enough qualified teachers who are able to teach the content and as a result you get many students who are a) compelled to do maths/science and b) taught by teachers who worsen the disengagement. In my eyes, if we look at the students who will be forced under this arrangement to do maths and/or science in year 12, a very very small percentage will actually end up anything maths or science related in university. In fact, from my perspective, if there are students who don't like the maths and sciences, then let them be. Forcing them to do it, after already giving them the opportunity to try it from year 7 to 10, isn't going reap much benefits.
Also, the article says "The global report card revealed that Australian students' rankings fell from 15th to 19th in mathematics and 10th to 16th in science." Then, as a result of that, my strong opinion is - Stop worrying about getting more students to do the maths and science subjects, by making it compulsory. Instead, focus on improving how we teach mathematics and science to current and future students, and focus on attracting more prospective science and mathematics teachers (especially those who are brighter and do have the capacity to teach things like 4U Maths, considering how we're seriously running low on teachers who can teach 4U Maths). If you focus on that, it will lead to enhanced learning and students getting more out of their secondary studies in the areas of science and mathematics. Then that will actually lead to more students actually choosing to study maths and/or science (both at the secondary and tertiary levels), which was the initial aim of the policy change.
EDIT - As mentioned by InteGrand, we also need to make changes to the syllabus, because that is also key to student engagement and so on and so forth.
