The whole point of insurance is to distribute risk. At some point, if coverage granularity becomes too high, insurance will just become pointless, right?
I think it's more subtle than that. It's also about symmetry of information.
If you for example do 23&me you might find it that you have a much increased likelihood of getting a fatal disease soon. Thinking about your family's financial future you might decide to get life insurance because of this new information. Your individual risk in this case is very different from the average, you know this and that's why you are getting the insurance.
This scenario if it became common also would break the insurance model because the insured pool suddenly wouldn't include people with average risk but tend towards higher risk. This would lead to higher cost for everyone who is insured. In an extreme scenario the cost might get so high that it only makes sense to get life insurance for people who know they are likely to die soon. Of course the likely scenario is less extreme, but this shows the principle nicely.
I don't think so, no. If I know for a fact that someone has a 40% chance of dying tomorrow, it still makes sense for me to sell them insurance valid tomorrow only, charging 40% of payout plus some margin. It also probably makes sense for them to buy it, to guarantee the higher payout for their family if they die.