Of course, being able to switch hit is great, but, it is not allways necessary. My point. You were a baseball mit in one hand, and can catch everything. Tennis racket also in one hand. Same side, forehand and backhand, takes care of everything.
I think if you get a few core ideas down on the side you like it, maybe two or three with a right lead and two with a left, you have a good palate to choose from.
Also, if you are right handed, train new ideas with your left. You’re right will get it automatically.
Or maybe I’m full of balony.
thought I would contribute
If you consider that the left side of the body is considered heaven (left hand earth point of heaven side - gathering) and the right, earth (right hand heaven point - active) are magnetic poles according to traditional taoist thought, it is no mean step to understand that the traditional left sideness of single whip is meant to follow the idea of gathering energy. Since, traditional Taiji chuan is steeped in Taoist spiritual/medical ideas, a good study on traditional Chinese medical concepts is a good suggestion for anyone engaged in this art.
Obviously, movements should be practiced on left and right sides of the body to use taiji movements in combat. 
Single Whip
Ok, I have my thoughts but why do people think that the single whip technique/posture is called “single Whip”?
Paul
www.moifa.co.uk
[QUOTE=Paul T England;1031008]Ok, I have my thoughts but why do people think that the single whip technique/posture is called “single Whip”?
Paul
www.moifa.co.uk[/QUOTE]
wasn’t it based on an older use of the term in Shaolin long fist? maybe Sal Canzonarri or bawang will have a more definitive answer…
incidentally, my teacher has found it given in an older text as “transforming the elixir” ( ), which is the translation we use;
single whip is a short metal rod
[QUOTE=Paul T England;1031008]Ok, I have my thoughts but why do people think that the single whip technique/posture is called “single Whip”?
Paul
www.moifa.co.uk[/QUOTE]
It’s 'cause every single time I use it I’ma whip someone’s azz! 
depending your facing
the right hand and the left hand will be pointing to the east and the west
both arms are like that of a long snake with the head and the tail.
it is also like a long whip and of course the tail part or end of the whip will be whipping.
similar move has different names in different styles
such as tong bei shi or thru back posture
golden pheasant shaking feather or golden rooster shaking head
jin ji dou ling.
tomato or to mah to
My thoughts on the subject has to do with the body mechanics. Fajing starts at the ground, goes up your legs, guided by the waist, up spine, to shoulders, out to hands, or whatever the weapon may be at the time. Fajing uses your body as though it was a whip… I was told that the names are clues to applications. You have unlimited"whips" to use, so it would indicate a single handed strike, a single leg kick, a single bump, etc with fajing… But to think that way limits the movement to one thing, when it is really many things. It can be used as its own complete arsenal. It can be used as Qinna, Shuai Jiao, a strike, a kick, even as a Qigong… The different styles have different ways of doing it and different possibilities in applications, as well as similarities in applications, so its hard to say. Best to not worry about the names, and worry more about the movement itself and how to use it…
When you crack a whip you throw it out and then pull it back.
With the single whip you can wrench their body in one direction and then strike it back in the other, kind of like cracking a whip. One of the applications. Plus the arms are flung out kind of like a whip.
I like the last two responses, thats what i am thinking, not application but body movement/fajing 
Most techniques have naff all to do with a specific application IMHO…
Using this method of analysis also means that no specific style is incorrect, yang, chen, wu etc all doing it correctly if they coordinate from their dan tien and use power from the ground up.
Paul
www.moifa.co.uk