String travel is not just up and down
Would take all day for those to load up with the dial up I have. Give details please.
Here's the thing about bows. They are mechanical, machines. Mechanically sound they repeat shot after shot. Hence, lateral/horizontal travel is consistent. Consistent meaning correct shot to shot, no error. Conclusion; No ill effect on accuracy.
Now, the compound bow has been around a few years. Every conceivable guide system for the cables has been tried, plus corkscrew cams that perform what the TRG system does. This was by Browning. Yes, draw bow and cams would corkscrew the cables off to the side. So, no guide rod, shoot through cables, double guide rod with no slides (cables slid back and forth on the rod), straight guide rods that minimized offset of cables (to the point fletching clearance became a issue), adjustable offset guide rods, plain guide rod slides, roller guide rod slides, roller guides, spring steel guide rods, stainless steel guide rods, carbon guide rods. and now the TRG system.
All the above applied to any one bow of the times have all done something, shot well and set records. Some records still standing.
Lateral/horizontal nock/string travel. If this was a problem I would think R&D would have eliminated this years ago. The compound bow and been up and running effectively for some 35 years.
Today, manufacturers are basically doing one thing, trying to catch your attention. Bows are basically perfect within themselves. Find one of the original articles of the Hooter Shooter; "Every bow we put through it shot groups of 2" or less at 60 yards." Another article of the Hooter Shooter; "/// accuracy wise, even weaker than desired spined arrows grouped outstandingly."
Bottom line; We are the problem.