Another who has never used one-sided cages. Now all my cages are stainless steel Kings shaped like the one in VegasTriker's post above. I reach down with both hands. Usually my right, but both when I switch the bottles. Now if I was small and rode a very tight frame, I could see one-sided cages but I passed on beyond that size long before I knew anything about waterbottle cages.
+1 to rm -rf and stainless cages. They don't break and don't shed bottles. I can put my bottle into the King cage crooked. When I look down 15 miles later, it's still there and still crooked.
Ben