An experienced florist doesn't usually require a gridded vase, but it does help an inexperienced designer to get the flowers to stay in place.
A greenery grid is usually the normal method for securing your flowers in the vase. My biggest objection with this is that I like my water to be crystal clear when finished - not contaminated with bits of greenery being forced below the water line.
A clear grid made with narrow clear tape is a quick way to START designing with the flowers first - and inserting your greenery last.
You need to be sure your water is thoroughly mixed with flower food and your sides of the vase completely dry before gridding your vase. Don't worry about overlapping - the lines are virtually invisible after the flowers have had greenery added.