I suppose the safest method would be to switch off a phone, or switch it to airplane mode, while driving. Would a requirement to use such an app while driving prevent that approach?
You can use an app like Offline Maps & Navigation that doesn't require the internet (after downloading the required maps)... and I think that Google Maps allows you to bring navigation instructions offline.
Sure, that's possible. But that means foregoing traffic alerts and redirections.
And it means you can't share your location with other people so they can track your progress. I do this on long trips so the people I'm driving to can see where I am without having to contact/disturb me.
Sure there are trade-offs, but anyways, I guess this app could be recording all the tracking data onto internal memory until you switch airplane mode back off and then transfer it to the insurance company.