I actually worry about this a lot. I think people living too long could be a very big problem. It's the kind of thing that could very easily create a kind of stagnation when it comes to our evolution. Older folks have a very hard time transitioning to the current age. Eventually everyone gets stuck in the past.
I've already seen firsthand how difficult it can be for the older generations. I had a very brief job once teaching seniors how to use basic functionality on their iPhones and how to create an account on Facebook and such. It's not intuitive to them AT ALL! Can you imagine what it would be like teaching a 200 year old to calibrate their own 3D-printer?
Death is a part of life; a very important part. I think as the average lifespan goes up weird unpredictable things will start happening, and it won't be good.
I don't think you have to worry too much about it. Insurance isn't likely to cover ongoing longevity treatment into perpetuity. There will be limits set in place that will only allow for the wealthiest elderly people to keep it going.
This is intended only for the upper class right now and will likely remain that way, since they control the laws of societies. I'd be surprised if this ever becomes an option for people outside of the wealthiest 1%.