Not sure the miners have it completely support free. Favourable depreciation, instant exploration write-offs, etc are pretty favourable in a capital intensive industry.
Exploration does not necessarily yield a result I.e. a mine. It is more appropriate to see it as a cost in my view rather than capex. It would be like the time spent at a real estate company committee meeting being capitalised because they may set up a new office in a new suburb at the end of it. The time invested exploring the proposition is not capitalised into the new venture.
For me the only compelling argument is that they make good on Australia's natural resources but so do farmers, surf schools and fishing charter operators.