Bitcoin ain't perfect, and you could say that requiring internet connection is one of the downsides.

And yes, theoretically, having the internet shut down woldwide(for whatever reason) could be a problem. Fortunately though, chances of such problem occurring becomes less and less by the daily because of advancing technology. Starlink seems promising, and Blockstream satellite already exists. And if Bitcoin adoption just continues to go up from here, expect new technologies to be created to decrease the chances of downtime in the future.