Recently I saw this company's ads on social media and happen to be at renewal time with my current health insurance, so I'm currently checking them out too.
The plans at Genki seem quite comprehensive, perhaps even covering scooter driving for unlicensed drivers and a lot of travel-related recreational activities like scuba diving. The limits are high.
For some of their plans, they seem to resell a service from a company called "DR-WALTER". There was a thread on Reddit asking about them and the founder replied, so they appear to have a strong desire to maintain their social media presence and brand image. That will come into play if there's an issue - it will matter to them a lot of you call them out in public.
Genki has 4.4 stars on Trustpilot, but it seems like DR-WALTER will be the company that approves and pays out claims so the experience there might matter most. DR WALTER has around 3.7 stars on Trustpilot, which is fairly high for this industry I think.
The types of complaints people are bringing (I read all the 1-stars) seem to be mostly related to communication and payment speed. It sounded like some of those people were short on cash leading them to freak out. If the company eventually makes you whole in a reasonable period of time, then the contract is fulfilled. I was looking mostly for complaints from people who were denied a claim when they thought they should be approved, and didn't see much of that.
I think I speak for most when I say that the #1 concern with any insurance company is whether they'll be there for you when you need them. Like you need half a million dollars to fix you up after a terrible crash or some kind of long term cancer event. Those are the situations that really wipe people out, and I suspect the kind of claims that insurers work quite hard to deny. I didn't really see any experiences with this, so time will tell.
The plans are a bit more expensive than some, but I think I'll give them a try and see how it goes.