Trade - are they really allowed to be so biased toward the supplier?

is it even legal (in Australia or elsewhere) to make such an absurd contract?

Yes, whence it is important to be judicious as to whether or not sign it. Without (me) knowing the specifics of Australian law, two parties are generally allowed to enter a biased contract. At that point, the contract becomes binding.

Legislative provisions might render a contract unenforceable. But these provisions are enacted only for very specific areas such as landlord-tenant or medical matters, whereas that is unlikely the case in less essential business such as trades.

By consenting to that clause, you might be making it more tempting for the supplier to arbitrarily increase your bills or to deliver something below the work you two agreed upon. Contract law is always premised on the covenant of good faith and fair dealing, and therefore you might ultimately prevail if the supplier incurs abuse. However, chances are that it will require you to engage in judicial proceedings, and you might not even recover the totality of your litigation costs.

The supplier's proposition of acting as your "true and lawful attorney" sounds unenforceable from the standpoint of lack of credentials to practice law, and flawed due to the supplier's obvious conflict of interest. I would be surprised if that language in trades' contracts is as common as you mention.

Save yourself that much trouble and get another supplier whose conditions are more equitable.

Trade - are they really allowed to be so biased toward the supplier?

is it even legal (in Australia or elsewhere) to make such an absurd contract?

Yes, whence it is important to be judicious as to whether or not sign it. Without (me) knowing the specifics of Australian law, two parties are generally allowed to enter a biased contract. At that point, the contract becomes binding.

Legislative provisions might render a contract unenforceable. But these provisions are enacted only for very specific areas such as landlord-tenant or medical matters, whereas that is unlikely the case in less essential business such as trades.

By consenting to that clause, you might be making it more tempting for the supplier to arbitrarily increase your bills or to deliver something below the work you two agreed upon. Contract law is always premised on the covenant of good faith and fair dealing, and therefore you might ultimately prevail if the supplier incurs abuse. However, chances are that it will require you to engage in judicial proceedings, and you might not even recover the totality of your litigation costs.

The supplier's proposition of acting as your "true and lawful attorney" is a non sequitur if the supplier['s company] lacks of credentials to practice law. I would be surprised if that language in trades' contracts is as common as you mention. Furthermore, that proposition is flawed from the standpoint of the supplier's obvious conflict of interest should a dispute arise between you two.

Save yourself that much trouble and get another supplier whose conditions are more equitable.