Insurance does cover negligence.
The insurer cannot (generally) prove the pilot did it intentionally, which leaves just negligence and this is covered.
The stuff where insurance will take a walk is where the paperwork is duff e.g.
- duff/expired CofA
- invalid pilot license/rating (though they will pay out if a plain PPL departs VFR into OVC002 and kills himself immediately, because flying at 199ft is legal if you meet the 500ft distance rule)
- N-reg not owned by a US citizen and thus CofA is void (etc)
I don't condone over-MTOW flight of course. But technically it does work - you need to understand what happens. For small excesses, say a few % over, nothing happens, but you need more runway. Each 1% on weight means at least 2% more runway.