There is nothing illegal about paying a bill in cash.
There is a lot that's illegal and unethical about accepting a "lower price for cash because I wouldn't have any tax or GST expenses". The offer inherently involves the commission of a crime, and by accepting that offer, you're facilitating a crime.
As long as I get an invoice, with GST listed, I'm not responsible for what happens after that. The tradie could still cheat on tax, but I wouldn't be a participant in the fraud.
But if I accept no invoice, or an invoice with no GST listed, which the tradie emphasises is unable to be used to obtain GST credits, then I'm also participating in the commission of a crime, and I'm unwilling to put myself in that position.
If you are, good for you. sanjayag was seeking opinions, I've given mine. As has been said, they're like bums, we all have one.
Perhaps if you'd started / qualified your reply with "in my opinion....", it would have read alittle less as if you were making a statement