Perhaps we are all barking up the wrong tree.
You could just do a spatial join on the new points from that day with a persistent county fc with the output in_memory with just the name field carried over from the county fc.
Then append that to a long term points fc.
You could then programmatically delete all that days features from the new points fc so you are working from an empty data set each day.
Roughly (I'm sure Richard will pick up on any errors):
import arcpy
# Establish parameters
new_features = # A temporary feature class that is reset each day
county_feature_class = # The county feature class used to get county names
historical_features = # A feature class you add new points to as they come along
county_points = arcpy.analysis.SpatialJoin(new_features, county_feature_class, "in_memory/County_points",
"JOIN_ONE_TO_MANY", "KEEP_ALL",[fields you want to cary over],
"INTERSECT", None, None)
arcpy.Append_management(county_points, historical_features, "NO_TEST",...)
When I tested is using GP tools within ArcGIS Pro it only took 7 seconds total for all the cities an counties in the US.