That area of Andersonville/Edgewater should absolutely not be down-zoned. As a 3 year resident in the area between Clark/Broadway/Bryn Mawr/Foster, most of the homes that have "historic character" will be, and are being preserved. That said, the bigger beast here is the elimination of units across Andersonville, the Edgewater community area, and Bowmanville to the west.
In my free-time I track unit gain/loss across the city, and the rough map below highlights unit loss from both rehabs and demos/new constructions from 2006 through July of 2018- with circles being rehabs and triangles being teardowns. Red/orange/yellow are neutral/loss of units, green are unit gains. Using the Clark/Broadway/Foster/Bryn Mawr boundaries, the area saw:
Rehabs (circles):
41 Instances
-15 Units
Demos/New Construction (triangles):
11 Instances
+6 Units
This area is already losing units, as are the areas south of Foster and west of Clark. The sad fact is that without zoning minimums in these areas, many of the 2-4 flats that exist cannot be rebuilt once they are gone. Chicago Cityscapes did a piece on the zoning issues related to this a while back I believe.