Those marks we all have witnessed can only form from friction. That's should be obvious.
As a 3C player, clean balls and clean cloth are essential for a well set up table to play with proper angles. Moral is, with this game, in order to have reasonably predictable angles, the entire system needs to be clean. The System includes the balls AND the cloth. Table design is another story. Chalk? Unable to go there.
So here's what we have. Plastic balls moving and skidding across a wool and polyester blend surface generating static electricity in the ball. Chalk dust is powdery, abrasive and the balls are attracting this abrasive dust. That's one problem. Maybe think of every ball is like 3000grit sandpaper.
The next problem to address is the cleaning process. Removing chalk dust is simple. Just run it under the faucet for 2 seconds or add soap if you like. That doesn't address the micro scratches. They must to be removed. Think of those scratches as an extremely fine file or 5000grit paper. Make a 70degree cut or whatever and you have 2 plastic files scraping each other. Notice those marks are fairly large compared to what you would think is the contact surface area.
This leads to burnishing those micro scratches out. If you don't have an electric ball cleaner I recommend the Aramith Ball Restorer. The Aramith Cleaner isn't aggressive enough unless you clean every ball every hour or less. Now you need 2 or 3 sets. I have 6, but 6 sets of 3, not 16. And I do have power.
The object is to achieve a mirror finish/like new surface on the balls. All of them. If you're not cleaning the entire set, you're pissing up a rope trying to keep the CB in good shape.
The last piece of the puzzle is the cloth. You must keep that clean. I clean my table every hour or so of play. On the rare occasions I have a guest over I just wipe it down with a very lightly damp microfiber cloth. If not I vacuum, then come back with the damp cloth. Squeeze as much water out as possible. Lightly wipe. No scrubbing action.
Lastly, someone mentioned Cyclop balls. I have a set of these for carom and they do last longer than the Aramith. The Duramith (sp) formulation sounds like they should last even longer. Unfortunately for me, Saluc doesn't offer this in their carom ball offering.
Friction is your enemy on this. Do what you can to eliminate it.
Short of adding coatings to the surface.