A search cursor like this could easily iterate through all the points and add them to a csv file for you.The key here is to use the "explode to points" method in the search cursor
import csv
with arcpy.da.SearchCursor(featureClass, ["OID@","SHAPE@XY"],explode_to_points=True) as cursor:
with open("outputFile.csv","wb") as csvfile:
writer = csv.writer(csvfile)
writer.writerow(["FID","LAT","LON"])
for row in cursor:
FID = row[0]
lat = row[1][1]
lon = row[1][0]
writer.writerow([FID,lat,lon])
Hope this helps!Matt