Telling people to stop using the Internet because it is insecure is bad advice. It is extremely unrealistic, like telling people to stop using cars and trucks because driving kills people every year.
However suggesting that we should change things to eliminate the risk is good. We could eliminate car accidents completely if everyone went over the automatic driven cars that communicated as a mesh network. The Swedish "zero vision" could be achieved, maybe even with todays technology, but it would be a massive undertaking.
Replacing BGP would be a similar massive undertaking. Just switching away from ipv4 to ipv6 has so far taken 20 years and we have no date in sight when we can start deprecating ipv4. From what I have heard/seen, a lot of people are somewhat reluctant to issue backward incompatible replacements of core infrastructure because they look at ipv6 and fear that kind of process. Even seen some pessimistic talks that argue that it is impossible and the only way to achieve changes in core infrastructure is with incremental changes that are fully backward compatible. I am not really of the view but I do understand their fear.
My advice to people is not to abandon email, even if I doubt much people would heed to the warning that email is unsafe for government, business, people and their family. People will risk it regardless. Thus I focus on what may help, imperfect as those may be. In the past that was PGP in the form of enigma mail plugin. Today I am keeping an eye on the new pretty Easy privacy which hopefully can outsource the security to a library that attempts optimistic encryption when ever possible.