With your current setup, you have too much travel, and the DS actually hits the frame, which clearly is bad.
The limiting cables DO fix that problem.
I don’t think they create any additional problems either. In essence all race suspensions have travel limits, it is just usually the bottom of the shock travel and not a strap. Your shocks are too long, and this strap fixes that problem.
So then you just need to think about what happens when you are using the cables. All the cable does is absorb the force which would previously have been absorbed by the axle pushing on the frame.
The only time these straps will effect the handling of the car is when the car is at full front drop. This will only happen to the inside wheel when turning at the limit. And when turning at the limit you have very little pressure on your inside wheel anyway. So even if you reach the suspension travel limit, your force on the tire goes from very little to zero, which is not that big of a change.
Now if you have a considerable preload on the strap at full droop, there will be a more drastic change, but I don’t think it would upset the handling of the car. It might even help, or you might not even notice.
Now the execution of these cables is a sketchy. I would not have used that type of cable clamps. They are OK but they have bolts sticking out really close to the tire. I’m also not cool with that steel cable floating around in the wheel well either. I have no doubts that this will find its way over to the tire at some point, which will not be good.
You would probably be better off with a nylon strap material like a seat belt or racheting strap material. Weld on one of those buckle/loop things to each end and now you have an adjustable strap that is not metal. This nylon strap would be much safer if it were to rub the tire. You could also put a big rubber band on the nylon strap to pull it away from the wheel but not interfere with it.