isshinryuronin
Senior Master
I think all the basics kicks, strikes and blocks should be practiced to a competent useful level on both sides. This will make you solid in any situation. Then, we can have a favorite "tricky" move or two that works best on our strong side such as a spin kick or other move that might be just right for a particular situation.You don't have to train the same technique on both sides. You can train different techniques on different sides.
If the opponent knows you can't throw certain moves from a certain side, he better knows how to enter on that side and not have to worry about defending that weakness. This allows him to devote more defensive attention to your other moves.
When the opponent knows you can throw various moves effectively from either side he must be twice as vigilant and will have more defensive choices to make, both of which reduces his reaction speed.
I am a strong believer in being "professional" and having strong basics on both sides.