I believe there are pros and cons to any solution you go with. Nobody that takes web development seriously routes all their website's DNS traffic through CloudFlare, AWS CloudFront, etc. without also understanding the risks of those services going down and taking their site down with it.
Personally, I choose to cache all my websites on CloudFlare due to the increased speed it gives my visitors and the decreased loads on my own servers. That said, my websites are not vital enough that I would care if CloudFlare went down for a day. It happens. The speed and load benefits greatly outweigh the risk of failure for me.
Other companies roll their own CDN because they need to be sure that if their CDN goes down, they have all the power to fix it. It's just whatever floats your boat. There's no silver bullet to any of this. Even if CloudFlare going down takes down "half the internet" with it, usually the most popular websites have their own solutions, and the 50% that is inaccessible may only affect 20% of people. For example, Netflix alone takes up 15% of all internet traffic. They have their own CDN and wouldn't go down when CloudFlare does. :D
