While fusible links will blow, protecting major circuits, they really act much like shock absorbers. They will take large spikes of current without instantly popping. This allows the main circuits to remain operational under a vast array of operating loads without blowing every time a "jolt" or short term high draw situation hits the system. Most fusible links have been replaced in today's cars with the more modern maxi fuse. These give the same "slow blow" operation the fusible link offered in an easy to see replaceable fuse style component.
As for Elan fires it's more likely to be fuel leak on to the distributor or carb spitting on to fibreglass or not disconnecting the battery when working on car.