Want to protect free speech in Australia?

I've seen some very interesting arguments from legal practitioners that the US's highly political constitution is a significant part of the reason their courts are so political, and that this is a good reason to have a much less political constitution like Australia does.

The US constitution says "you have the right to have weapons" and also "you have the right to freedom of speech", among many other things. Australia's constitution is almost entirely dedicated to stuff like "the Commonwealth has the power to make laws about trade between states" and "politicians must be Australian citizens exclusively".

So in America you get the unelected Supreme Court making very politicised decisions like inventing a "right to privacy" based on the right against self-incrimination (and other express rights), and then taking that right to privacy that was invented by unelected judges, and using that as the basis for inventing a right to abortion. Now, like me, you might think having a right to abortion is a good thing, but in this case the way it was enshrined is obviously bad, because it was invented by unelected judges, and decades later was removed by future unelected judges, rather than the actual elected representatives of the people enshrining it in law.

Yes, I think we should have a bill of rights that explicitly enshrines a number of important civil liberties, including free speech. But I'm not sure that a conditional amendment is the best way to do that.