My point was: I see no reason why we couldn't accomplish everything Cloudflare does without a central authority. Markets are able to solve just about any problem without any central person pulling the strings. Case in point: the internet.

This is such a weird statement. I totally agree that markets can solve this problem. They brought us CloudFlare!

(and a few other companies that offer similar services)

Sadly, all of them appear to require Big Internet Infrastructure. This isn't a problem you're going to solve at the wifi level.

I'm speaking specifically against the statement that Cloudflare, acting as a central authority, can solve problems that cannot be solved without a central authority.

As has been pointed out there are alternatives to cloud flare so it’s not a central authority.

Is the internet a good example of free markets and capitalism? I always perceived the glory days as more akin to communism.

There’s nothing about capitalism that prevents, or is anathema to companies, organisations or individuals from collaborating or pooling resources. Communism is a specific political and economic system with explicit and deliberately coercive communalising policies. It doesn’t have a monopoly on community forming or coordinated community action or the pooling of community resources though.