Ok a more controversial question: if we're saying all the as are the same, can we not consider the system as a whole and write f=ma based on the direction of motion being up-right-down? Rather than using simultaneous equations?

This is a very interesting question. I would say that mathematically we can; I don't see anything wrong with doing it like any other connected particles question. But the exam boards categorically do not give the marks for it (it's come up) so do not suggest this to your students.