The rod and the reel and the line are secondary to the fly, in terms of hooking and landing a fish. If the fly is not there the fish can not eat it. So there must be a fly or there is no fly fishing. Of course, the other tools are also critical process. a leader is needed to hold the fly to the fly line without tipping the fish of to the presence of the fly line, and eventually to tether the fish to the fly line. The fly line is needed if you want to fish further than about 15' (which is aproximately the distance that I can throw an unweighted fly by hand), as the fly needs to be carried by the weight and momentum of the flyline to be delivered to fishes location in the river.
A person could cast a fly, leader, and fly line by hand and catch fish(Lee Wulf famously accomplished this catching a salmon, long before I was born), but this decrease the efficiency of the process to such a degree that it would quickly become frustrating. I, infact, strive to find efficiency in my fishing exploits, though not to the degree that I would take upnymphing or gear fishing on a regular basis. Anyway, I digress, a flyrod is, in my view, a necessary tool in the delivery of the fly.
I have caught many fish with either no reel, or a malfunctioning reel, and while this is also possible, it is again, inefficient. Reels are necessary too.
Each river and each season bring their own challenges and requirements, when it comes to getting your fly in front of the fish you are after. Sometimes fish want to eat small (#3-#10) flies on or just below the rivers surface. Other times fish prefer a big fly (3"-5" long) fished 3'-4' below the surface, and some time even deeper than that. Some runs have fish sitting just a few feet off the bank, while others require a very long cast to get the fly out to where the fish are.
The goal is to figure out what is reguired to find the fish and to then accomplish the delivery of the fly to the fish in the most efficient way possible. Such as fishing a skagit head on a small, tight-to-the-bank, spring river.
Above and Below: Skagit Casting a CF Burkheimer 7133-3 w/550 grn Comapct Skagit. I am casting about a 5" string leach on about a 5' leader and with a 9' T14 tip.
My favorite way to fly-fish is with a two handed rod. I like to cast long belly lines especially for summer steelhead out on the clearwater and the snake. Although I often fish both Skagit and Scandinavian heads very often throughout the year. Last year, infact, I fished only a Scandinavian head on the snake, where I would normally prefer a long belly. So... there are a lot of ways to skin a cat, I think the best way is to find what you enjoy the most. That way you will spend more time fishing, and less time being frustrated.
Below are some additional casting videos using various rods and lines for different purposes. I do this as a general reference.
-------------------------------------------------------------
Below: I do a snake roll with the same outfit.
-------------------------------------------------------------------
Below: Doing a Snap T with the Sage 6110-4 and a Compact Scandi - Grande Ronde.
Above: Tom Town performs a left handed single Spey w/ a 16' Bruce and Walker and a Next cast Fall Favorite. Oconto River
Below: I perform a cross body single spey with a G. Loomis 15' 7wt and a 65' Hardy MachII