Look here, you said "potential vulnerabilities". if we are sure that there are no vulnerabilities in the system, then we can connect to the internet.
Nobody can be sure there's no vulnerability in system, when new vulnerability keep discovered as time progress. For example, there were 11 new CVE (based on published date) for Windows 10 and 15 new CVE for Linux Kernel[2] in last month.
Anyhow, reading all of the replies and none agreeing with my point of view, i have started to feel scared.
I assume that's because people who replied either unable to afford to lose their coins or being far more cautious, especially for saving all your coins.