Is it possible for a non-towered airport to have keyhole extensions Class E starting at the surface? (skyvector.com, modified)

The Springfield, OH airport, KSGH, is a non-towered airport with both precision and non-precision instrument approach procedures. To support these approaches, there are a couple of "keyhole" Class E transition areas; however, these particular Class E transition areas start from the surface (magenta dashed lines) depicted on VFR Sectional Charts.

I'm really confused how the Class E areas extend from the surface when the airspace directly over the non-towered airport is Class G. Is it possible that the VFR Charts are in error and the magenta dashed line should be removed or converted to a magenta vignette indicating that the Class E starts at 700' AGL?

There are several indications in my mind that this is simply depicted as an error on the VFR Sectionals:


The VFR Sectional says, "See NOTAMs/Supplement for Class E (sf) eff hrs"; however, when consulting the Central Eastern Supplement for KSGH, there is no "Airspace" item listed under the airport.  Which substantiates the VFR Sectional chart designation that the airspace directly above the airport is Class G.
Since there is no "Airspace" in the Supplement (nor NOTAMs), there is no "effective hours" as the VFR Chart suggests that there should be for the two depicted Class E (sfc) areas.
As depicted, it appears as if the a pilot could enter Class E controlled airspace and then quickly transition out of it and into Class G uncontrolled airspace as they continue on the approach.  This doesn't make sense when you consider the intent of the Class E transition areas are to help IFR traffic be provided separation from Class G traffic.
The Airman's Information Manual (para 3-2-6.e.2) describes "Class E airspace may be designated as extensions to Class B, Class C, Class D, and Class E surface areas."  It does not include Class G airspace in that list of airspaces that Class E may be designated as an extension.
The AIM (para 3-2-6.e.2) goes on to say, "Surface area arrival extensions become part of the surface area and are in effect during the
same times as the surface area." Since there is no surface area in effect, it seems to be another indicator that the Class E (sfc) is also not in effect.


Can anyone explain how it's possible for these two Class E (sfc) areas to be legitimately marked, or are they simply errors?
There was a control tower at SGH which closed. The FAA issued a rule which removed the Class D airspace as of December 10, 2015.

This leaves the class E airspace chunks. As you noted, the Chart Supplement for SGH has no information about the airspace, and FAA Order 7400.11A (the current version of airspace definitions) states only that, after an initial NOTAM announcing the effective dates and times, (p. E-183) 


  The effective dates and times will thereafter be continuously published in the Airport/Facility Directory.


So, is the airspace between the surface and 700AGL in these two areas class E or G? I'm not a lawyer, but I think you could make a strong argument for the airspace being class G, unless the chart supplement gets an update or a NOTAM is issued.

Finally, to the question: why are these two areas there? Two thoughts come to mind.


The class E extensions existed alongside the class D airspace, and nobody thought to remove them. (This is the most likely, to me.)
There is some other operational reason for the class E airspace. There are instrument approaches to the field, though they terminate well inside the radius of the two airspace segments, so that's not very likely. Also, the class D airspace could be reactivated by NOTAM if a high-traffic event at SGH were to occur; the class E extensions could be part of that. However, both of these options are really stretches - my guess is that we've found airspace that someone just forgot.


2019 update: those extensions are no longer visible on the sectionals:


(skyvector.com)