For US government employees, records of those emails should exist on the other employees' end, at government-run servers. UNLESS, there was a whole network of high-level US people using private email addresses to circumvent record keeping. THAT would be a major conspiracy, and one that could more easily be unraveled than the concentrated misdeeds of one person (i.e., Hil).
And THAT is what I believe happened here. This wasn't the entire State Department. I believe the number of individuals part of this is rather small, but consists of some very well-placed and useful people that she didn't want to get caught colluding with.