Will insurance cover replacement of potentially dangerous cracked concrete porch floor over an old coal room?

In all likelihood no, you will need to take care of this yourself. Homeowners insurance policies cover things that are sudden and accidental. This would be things such as fire damage, smoke damage, water damage, theft, graffiti, wind damage, etc. Things that cause damage in a brief period of time and weren't intentionally caused by the homeowner. What they don't cover is ongoing maintenance issues.

Unless your concrete porch was damaged in an accident, which doesn't sound like it's the case from what you wrote, then the insurance company is going to consider this to be a maintenance issue and thus not covered by the policy. Homeowners are expected to take care of maintenance issues as they occur in every home and aren't accidental or sudden in nature. If homeowners neglect things like an old, bad roof that lets in water, mold issues develop, and so on no insurance company is going to pay out on a claim for that sort of thing.