Not only if the internet dies. If the country or countries managing the AI decide they don't like your country and ban you from using their (major) AI providers, in a world where most knowledge and work tanks will require access, you're screwed.

Not even talking dictatorship scenarios here. The USA might simply decide it doesn't like your country. Or maybe heavily cripple the models you can use, or censor them, for whatever reason.

I guess this is an argument for local AI. Probably not feasible for the less technically savvy.