You are mixing things up. Using google or M$ for government email services is not against going analog, the problem is that we are paying ubercompanies to handle our data, even important ones. If government instead relied on open source, self hosted services, there wouldn't be much of a problem for using emails only.
As for not being able to use cash as much, you are right, that's a problem if one wished to go "analog".
Ever spilled a drop of diesel? Exactly that happens