Classified and unclassified information do not mix. They don’t travel in the same streams through the same pipes. They move in clearly well defined channels so that never the twain shall meet. Mixing them together is unheard of and a major criminal offense.
If you end up with classified information in an unclassified channel, you have done something very wrong and very serious.
Accidentally removing a single classified message from controlled spaces, without any evidence of intent or exposure to hostile forces, can get you fired and cost you your clearance. Repeated instances will land you in prison.
Every hostile intelligence agency on the planet targets senior American officials for collection. The Secretary of State tops the list. Almost anything the Secretary of State had to say about her official duties, her schedule, her mood, her plans for the weekend, would be prized information to adversaries.
It is very difficult, in fact, to think of much of anything that the Secretary of State could be saying in email that we would want hostile forces to know.