Not necessarily. Having an “open web” doesn’t require you to be a network peer. You have to pay someone to bring the bandwidth to you. A CDN just moves that connection point a little. It actually allows you the freedom to run whatever server you want with much lower hardware and bandwidth requirements — even if 100% of your traffic were true humans.

That said, a CDN is only good for standard web traffic, not some custom game/chat/video service you might invent, but then again crawlers aren’t hitting those.