Now, I know the advantages to practicing Kata's (balance, internal energy etc. etc.), but I can't see the point of one and two step sparring. Or as I prefer to call it, Scripted Fighting. Never, not once while sparring have I used one of the techniques tought in 1 and 3 step sparring. The only thing I can see gained from these is that your training the muscles to automatically respond in the situation were someone throws a right reverse punch while stepping through with their right foot. We all know that doesn't happen except for during running haymakers; In which case a side kick would be more effective.

The negative side of these "Scripted Fights" is a false sense of confidence. What if the punch is coming from the left side, sure our training will keep us from getting hit, but why do we only practice one side? Another minus I see in this training is that if you fight someone with any training at all, then those techniques are ALMOST (not completely) useless.

Hopefully some of you guys will have some insight as to what advantages I'm not able to see while doing these three 1 and 3 step sparring.

We practice our one and three steps from both sides. And, I think if you really analyze how you are sparring, you will find more of these techniques being used than you think. The blocks and counters learned in the one and three steps should be useful during sparring, even if the opponent is not doing a step through attack.

Like mentiooned above, you do the 1-3 step sparring to form a basis for free sparring. Like everything else, practice, practice,practice, eventually it becomes second nature and then you do it subconsciously. Also the 1-3 step sparring is good for people just into MA's to get acclamented to having someone throw a punch at you.

I think that 1 and 3 step sparring, like most MA drills, can be helpful but can also be over-emphasized. For example: If you never train for self defense in any other way that straight punches while the attacker steps into a front stance and leaves his hand there for you to play with, then the training is very limited in how much it can help you on the street. I like to use one step as a stepping stone on the path to more realistic self-defense. It has its place, but should not be over-emphasized.
We all have different opinions, this is mine.