What requirements aren't met, that would designate an airspace to be Class E instead of A, B, C, or D?
The simplest answer is that Class E doesn't have a control tower, and the others (Except A) do.  

Think of Class E like it's "Class A", but just at the lower altitudes. Both A and E are basically "wide swaths of airspace, not really near a major airport" with control provided by the Area Control Center (similar to ARTCC in the USA). Whereas B, C, and D are designated at airports with Control Towers. The only real difference between A and E is that no VFR traffic is allowed to enter Class A.

Although you're right that VFR traffic does not need to communicate with ATC in Class E, be careful about using the phrase "to them, it's uncontrolled airspace".  It IS still controlled airspace. VFR traffic does not need (nor sometimes want) to be controlled, but that does not make the airspace "uncontrolled".  "Controlled Airspace" is a term one will likely encounter on exams, and one doesn't want to get into the habit of calling it "uncontrolled" just because one is a VFR pilot.