I didn't check the associated paper, only the article itself.

For now this sounds a lot like a curiosity, but this might be useful in the future - if the healing happens under less than ideal conditions, faster, and for wider cracks, it could increase long-term resistance for key applications. I wonder if some vibration (including gentle heating) couldn't also help.

A potential issue is however air. The experiments were performed with platinum (that doesn't give a damn) in vacuum, but in real life you got oxygen and even nitrogen potentially leaking into the fractures, binding themselves into the metal, and saying "NOPE, IT'LL STAY LIKE THIS". So your best bet would be perhaps alloys that are harder to oxide, or even crystalline structures that already have oxygen.