The internet seems resilient enough for all intents and purposes, we haven't had a global internet-wide catastrophe impacting the entire internet as far as I know, but we have gotten close to it sometimes (thanks BGP).
But the web, that's the fragile, centralized and weak point currently, and seems to be what you're referring to rather.
Maybe nitpicky, but I feel like it's important to distinguish between "the web" and "the internet".