Yes its a problem. Electrically, induction, as explained above. But you've also created a vibration control problem. Hard to say which is worse. Usually these things are not so bad or obvious but taken to the tight binding degree I would expect a very easily noticeable improvement simply by removing the zip ties and letting the cables lay with a little space.
Ideally, and as much as possible, all the cables should be at least a few inches apart. Crossing at right angles is better than running parallel. This is all for induction and noise. Electric currents always produce magnetic fields. Magnetic fields are weaker with distance according to the inverse square law. Moving cables twice as far apart results in 2 squared or 1/4 the field. Right now at near zero spacing going to even one inch lets say they're four times as far apart that's 1/16 the noise. That's the electrical part.
Vibration, you can change the sound of even just one cable simply by putting a bunch of zip ties around it. The whole cable is vibrating with the signal. Its hard to notice with IC and PC but put your hand on a speaker cable some time you will see. Especially with even a little bass it is pretty freaking obvious.
If it is detrimental to performance, are there any alternatives. Can anyone recommend a solution to the problem assuming a problem does exist?
You're already doing it right with cable elevators. The minute you remove the zip ties and hear the sound open up you will know you are on the right track. The solution is to think of all these cables as flexible water hoses. You wouldn't want your hoses all straight and bound together with tight turns. You would want the water to flow unimpeded in nice smooth graceful curves.
I could be more OCD but this will give you some idea what I'm talking about.
https://systems.audiogon.com/systems/8367#&gid=1&pid=8