VCE maths is not essential in the sense that it is necessary for your life skills. VCE however is all just signalling to universities about your skills and abilities. For some courses (things requiring a portfolio of work/med/etc.) there are interviews and other considerations, however for most courses, differentiation of students is about the scores that students get in certain subjects and overall. Maths is not easy, especially methods and particularly spech. But even if you forget everything you've learnt in the classroom, what doing a maths subject shows is that you've been able to slug through a hard subject and work hard and have a certain ability in the sphere of numerical reasoning.
This is what doing the maths subject indicates, and why is it used a a pre-req. For some courses maths skills are directly used so it makes sense that it is a pre-req, but even i you aren't using the maths skills directly, the generic numerical skills can be important to succeed in that course (e.g doing science, but majoring in say biol) even if higher level math proofs aren't needed.
I definitely agree that maths is not the only way that analytical skills can be developed and proven, but written analytical skills are very different to numeral ones and are useful in different contexts. It's definitely possible to be good at one and not good at the other, even though both require you to 'analyse'. Myself as an example, i'd consider myself pretty ok at maths, but shocking at written analysis. If i were doing an arts degree i would be failing, and that's just because my written analysis skills are shoddy to say the least.
Having said that, they don't just put maths pre-reqs onto courses for lols. They do for a reason (you need those skills) and if you haven't done maths there are lots and lots and *lots* of courses that are still open to you! and tbh, they're courses that you would probably enjoy far more, and do significantly better in if you don't like/aren't good at maths!