My theory is that the metal tape on flatwound strings has a slightly rough edge, far too small to see, and that's what catches our skin when the strings are new. Would also explain why it's more noticeable with some brands than others.
The cure is play time on the strings. You play them, the rough edges wear down. No longer grabby.
There is no way that simply playing your bass with your bare hands will wear down rough metal edges. You might ultimately fill in some of the gaps in the rough edges with skin, oil and dirt, which will give you the perception that the strings themselves are smoother, but there is no conceivable way that the skin on your hands will work as a substitute for sandpaper or steel wool.