I have a question about high or low kakari to a stone at the 4-4 point. It seems that if the opponent responds with a pincer then a common joseki is to invade the corner 3-3 point.

So the question is: if the pincer seems to be a likely response, why not just omit it and invade the corner directly? It seems pointless to play a stone which is most likely to be wasted.

However, as far as I know 3-3 invasions don't usually occur until mid-game, when there are no larger points. However, kakari are quite common in the fuseki. So I'm confused as to why a 3-3 invasion is too small for the fuseki, but a kakari which probably leads to a 3-3 invasion is widely used.

I might not have explained this very well...

Another reason for the approach first is in case black plays tenuki. A direct 3-3 invasion that black ignores transposes to the well-known san san josekis where white plays 3-3 first and the black covers with the 4-4 point. In all these cases, white takes firm territory in the corner, but black gets to build good thickness on the outside.

transposition example  

On the other hand, if black tenukis the approach, then white has the additional option of making a nice double kakari of either the double low, or high-low variety (with at a). Both double kakaris really hold black's feet to the fire as now it's not so obvious what to do with the black hoshi stone. Thus, the approach gives white more flexibility.

3 tenuki