This would be difficult and I suspect overtly complex if implemented in modelbuilder, a python solution would be much easier to run.
Here is the code that will achieve what you need:
table = r"C:\Scratch\fGDB_Scratch.gdb\test"
# Creates an array using all fields in table
array = arcpy.da.TableToNumPyArray(table,"*")
# Create a list of field names
lstFields = list(array.dtype.names)
# Remove OBJECTID from list
# You add other fields to remove here, eg. text fields
# Compute mean and if it falls below limit add to delete list
print("identifying fields to delete...")
toDelete = list()
for fn in lstFields:
if array[fn].mean() < 3.6:
# Drop fields
Once you have modified this code to your case drop this code into the Python console window in ArcMap or run it from an IDE.
In my test scenario I have a table and I'm checking the mean of the fields to see if they are below the value of 3.6, obviously adapt it to your scenario. I would recommend you do this from a backed up version in case your logic was wrong. My test table was this: