So I have been reading about line pinch when using braid. I use braid on almost all of my setups and have line pinch (or digging in) issues once in a while as well. I was thinking that if (and please excuse my lack of terms here) the thing that goes back and forth in front of the reel was geared to move across and back faster, then the line would overlap at an angle instead of inline with the line on the spool and would be less likely to dig in. Am I crazy? Any drawbacks to this thought?

Daiwa PE special reels do just that. The downside is that if you put a huge amount of pressure on the reel the levelwind is more likely to fail as the higher gearing is less powerful. 

 

Thicker braid cures digging in issues, so like anything else, there's a compromise to be made.

Daiwa PXR also do that.

I spooled up two reels with 15lb seguar smackdown braid & have not had any digin issues with it at all. The line just lays flat like mono.

When Spider Wire was the big name in braid they came out with an "X-wrap" reel that did just what you are saying. It was kind of a gimmick that obviously fell by the wayside. Good, round braid of an appropriate diameter spooled snuggly will be very manageable.

The line has to come off just as it went on so I would guess a lot of side to side movement would kill casting distance. A straight spooled line would come off linear and smoother. So now in order to get the same distance, you have to cast even harder wich will bring more problems. Just a thought.

Digging in issues come more from it not being put on with correct tension and cheaper braid.  If I have to pull a lure free from a snag I may encounter this slightly, but a quick cast out and reel in to repack the braid typically cures the problem and that is only when fishing lighter lures where there isn't as much drag and weight.  But like stated above, you spool and pack it on correctly and use a quality braid, you shouldn't have this issue.