The problem here is that the tiling schemes between WKID 4326 and WKID 3857 are different; that is, the cached tiles differ between them in terms of tile width/height, scale thresholds at which the tiles were generated, X and Y origin, units, and technically even the coordinate system properties. To be specific, one example here is that the WKID 4326 uses decimal degrees and WKID 3857 uses meters. Another example here is that, if you look at the technical differences between these two WKIDs, you'll see they are inherently different despite the fact that they are so similar:WKID 4326ArcCatalog projection definition for "WGS 1984 Web Mercator.prj"Name: GCS_WGS_1984_Major_Auxiliary_SphereAngular Unit: Degree (0.017453292519943299)Prime Meridian: Greenwich (0.000000000000000000)Datum: D_WGS_1984_Major_Auxiliary_Sphere Spheroid: WGS_1984_Major_Auxiliary_Sphere Semimajor Axis: 6378137.000000000000000000 Semiminor Axis: 6378137.000000000000000000 Inverse Flattening: 0.000000000000000000WKID 3857ArcCatalog projection definition for "WGS 1984 Web Mercator (Auxiliary Sphere).prj"Name: GCS_WGS_1984Angular Unit: Degree (0.017453292519943299)Prime Meridian: Greenwich (0.000000000000000000)Datum: D_WGS_1984 Spheroid: WGS_1984 Semimajor Axis: 6378137.000000000000000000 Semiminor Axis: 6356752.314245179300000000 Inverse Flattening: 298.257223563000030000I've read recently that Google Earth doesn't always have the best reproject capabilities. Sometimes it works, sometimes it doesn't. Clearly in the case of WKID 3857, it doesn't. The only way I can really think of to "reproject" the WKID 3857 service to display correctly in Google Earth would be to reproject is intentionally by re-publishing it in your ArcGIS Server instance locally. In other words, cascade the service... which is not only unsupported by Esri but also unpleasant in terms of visual quality and draw time performance. In the case of doing this, you would add the external WKID 3857 service into a map document and then alter the data frame to be WKID 4326 before publishing the map document.