I think others have given reason to leave the mortgage with the bank - easy/cheap access to revolving credit facility if you need it.
That may not be the case depending on how old the original loan was. I missed clearing a POSB loan before ANZ took over. Then found that ANZ had a $250 fee for early repayment and if I wanted a new loan I'd have to start from scratch.
At the moment I'm trusting that even an Australian bank wouldn't try to screw me over unless I owed them something. One thing that occurred to me is they can transfer their mortgage to someone else. Maybe there's scope there for something. In the UK it seems that the fee for mortgage repayment includes the bank discharging the mortgage.