Well the current way involves paying for a bunch of non-value producing busy work by insurers, lawyers and a ton of expert parties relevant to the litigation process.
There's probably some combination of "everyone just posts up a bond into a fund to cover this stuff" plus a really high deductible on payout that basically deletes all those expensive man hours without causing any increased incentive for carnage.
Events like these are a VERY rare exception compared to all the shipping activities that go on in an uneventful manner. Doesn't take a genius to do the napkin math here. Whatever the solution is probably ought to try to avoid expending resources in the base case where everything is fine.