Functionally it makes no difference whether you split near the middle or not -- a truly random selection would sometimes end up with a pile of one, and that's totally fine. As long as you're not trying to game the system by, say, specifically counting out the sticks to get the outcome you want, it makes no difference. (and if you're doing that, then what's the point?)

Splitting closer to the middle does make it easier to avoid unintentionally counting though. If you make the same splits every time, you'll get the same outcome of course.

Philosophically / spiritually speaking, "don't think about it too much and just split wherever feels right" is the simple answer. Keep in mind the question you want to ask when you make the split and let whatever happens happen. Close your eyes if it helps you focus.