Everyone has agency, stop pretending one of the richest and most privileged people in the world just doesn’t have any other choice.
The crown is not a person, it cannot choose anything. As said: If Charles abdicates, Parliament will just recognise the next in line (William) as King. And push come to shove there's no end to that line.
Tell them “no thank you, I don’t think my role as king of a colony is appropriate”.
First off, Australia is not a colony, it is an independent Kingdom. Secondly, it'd still be up to Australia to then abolish the monarchy, or force-retire him for behaviour unbefitting for a king and go with William, or whatever.
The monarchy exists because people are lazy and just let it keep existing,
Then blame the people. Blame them for being lazy. Blame them for not agreeing. But why blame a monarch for not needlessly causing a constitutional crisis? He's a mascot, he's doing his job just as in other countries a President is doing their job, and when you compare what he says and does before and after coronation it also becomes obvious that he's playing a role. He literally shut up about absolutely everything ever since he got that crown.
And he did quite some of that indeed before his coronation. Couldn't shut up, some would say. Among other things, he's never been opposed to Australian republicanism. Now he's bound to protocol, and the protocol says that the King is not to voice any even remotely political opinion whatsoever. He can comment on how nice the food was, that's about it.
Regarding wealth he's something like the 2000th wealthiest person on earth. Theoretically, can't find him on the billionaire list though he reportedly just about makes it. Lots of people have inherited more money and done way worse with it. I don't think it should be possible to inherit that kind of fortune but that applies in general, not just to monarchs.