The system is most definitely broken. We are a few years off it, but will be leaving England rather than allowing our children to be secondary schooled here.
As a teacher in a core subject, I was shocked when I first heard of it being taught by non-specialists as it didn't happen when I was at school. However, on reflection I partially agree and disagree with points made in this thread.
I do think that a good teacher is a good teacher, not directly related to their degree class - have seen plenty bad teachers with excellent degrees.
I am astonished by the assertion of many in this thread that a sports Science degree automatically qualifies you to teacher biology. There's a lot more to biology than human physiology.
I have managed to avoid teaching outside my degree specialism (other than KS3 across my faculty) throughout my career thanks to being plenty enough in demand (shortage subject) and as a professional (haha to that these days) would be concerned about my ability to deliver a subject I don't even have a GCSE in to what we should see as an acceptable standard, support misconceptions, being able to address questions and stretch the able.
However, as a realist, we have a very real recruitment crisis. If I were in charge I would make a new rule of +1 level - ie to teach a subject you must have studied it to one level further than your students. With a decent GCSE pass you could do KS3 in that subject, if you passed A level teach the GCSE... That way you would at least be able to provide some insight beyond handing the kids a textbook and BBC bitesize.
But education is broken. I really do worry it's too late.