As for paying back mortgages, well not if people cant pay them and not if the mortgage is held in a bucket company, the banks will never get money for it. All you have to do is have a $200 bucket company with a couple of thousand in it.
LOL bucket company, next time form a $2 pty ltd and apply for a loan and see if the bank requires collateral from the directors. If the scenario is what you painted then every listed would not need equity capital raising and just know on the bank's door with all that easy cash.
The big 4 are safe than your tax payer dollar. Should another proverbial 'S hit the fan', whoever is in Govt will collaborate with RBA to proactively manage the economy like any crisis. The banks make up a very weighted top 200 index, if they fail the confidence effect will render the most profitable gold operation co the same sell down as the consensus.
What are you going to do with your coins? If you use the hammer to think out that coin, you instantly lose the collector's premium.