Crossing your line:
- takes up more spool space which = less line storage which = less reach,
- takes up more spool space which = a over filled spool which = more chance of winch breakage due to jamming your line (think about what happens in a side pull situation)
- it provides an uneven spooling surface = less consistent pulling power (think about the additional power you have with an empty spool vs a full spool, then look at how crossing your synthetic line makes an uneven surface), a minimal issue but still relevant.
- Puts small 'kinks' in your line. Synthetic line is strongest in a straight line, kinds = not straight. A minimal issue but still relevant.
- Also spooling your line with the 'neat' method gives you a consistent line exit angle from your winch. Crossing your line back and forth does not provide a consistent line exit. This can create problems with the line unspooling nicely especially on side pulls.
If you have issues with pulling so hard with your winch and synthetic line that you are splitting wraps and pinching your line then you need to take a few extra seconds when you are respooling your line and put some tension on it. I have very very little issues splitting wraps, even with only using hand tension (I do put my back into it). I've seen plenty of steel cable split wraps and get pinched too.
ETA: Think of this too. Your line will not spool criss-crossed when winching in, so after use you will have to unspool your line to the manually respool it in in a criss-crossed method. Why not at a minimum spool it as hand tight as you can get it then, or leave it spooled in as it did on it's own as long as the line is not stacked?