Insurance is just one of its weaknesses. I doubt that there is insurance on the gold stash for it would open a can of worms that State Street would want to avoid. The insurer, of course, would want to know about safety, access, audits, claims on it, etc to even come up with a premium for the insurance. Now, State Street would never accept such intrusion, in part because the gold stash is probably used for all kinds of shady purposes, including backing shorts.
Just read the part in GLD's prospectus where the custodian subcontracts to subcustodians but has no right to audit or visit the subcustodians' vaults. It then requires third-party audits. So we can have the custodian own or pay off the third-party auditor to give a clean audit, while knowing that the subcustodian leases out the gold into the market.
If GLD shareholders suspect so and ask custodian to prove otherwise, custodian can simply say "we have no right to check the subcustodians, see the prospectus, but here is a clean audit result" however laughably compromised. If GLD or State Street goes bust, no holder of GLD has any claim to any gold. GLD holders simply become unsecured creditors along with all other creditors, with no precedence in bankruptcy court.