Jim Macklin wrote:

Instrument approaches are published for Class B,C,D and E
airspace. An instrument approach requires controlled
airspace and traffic separation. Class G is uncontrolled
and although there may be a Class G airport, the instrument
approach is conducted in the Class E over laid above the
Class G.


At uncontrolled airports instrument approaches are typically not
contained entirely within controlled airspace. Check some of them out
against a sectional and that will become apparent.

Where the feds considered it essential to have the entire procedure
contained within controlled airspace, they establish a Class E surface
area. Class E surface areas are unusual.