Distortion from Audio Rack ??

Unfortunately, everything in your room will affect the sound your get.  People go to great lengths to have as little between the speakers as possible.  Stuff between the speakers can vibrate and will always act as sound boundaries and/or reflection points.

I've found that people in the hobby that go to the trouble of taking care of their room FIRST before equipment upgrades have the highest level of satisfaction.  I would get the best quality dedicated audio rack you can afford and go from there.

I wouldn't hesitate the replace the wall unit.  Also, by removing it you open up the possibility of hanging some proper wall treatments around your speakers.  If you think your system sounds good now....try that!  Have fun and good luck.

There are a couple approaches to racks. One is a sturdy rack with individual dampening solution for each components on it, or a fully dampened rack. I have typically taken the former route. You are in a good position to do that as well.

You can now isolate each component. For some of my components I use vibrapods with a Black Diamond shelf atop that... and springs (Nobsprings, Amazon). For my turntable I have a Silent Running Audio Ohio Class custom isolation platform. 

Depending on how much space and your patience, you can experiment with the hundreds of vibration control devices on the market. You will likely be able to isolate each component from the rack and improve the sound quality. I'd start experimenting with inexpensive devices. Get a feel how much sound quality is to be gained. 

Keeping the Cabinet if it is a appreciated furniture item is to be encouraged.

Improving the Cabinets Interface within the Room, as a support for audio devices is quite straight forward.

The Cabinet can be sat on a low profile Sub Plinth with an Isolator Footer between floor and Sub Plinth and Sub Plinth and underside of Cabinet. The Sub Plinth can have a Cherry Edging Bead to keep the match in keeping with the furniture.

A Sub Plinth and Sub Sub Plinth will have a improved impact on the managing amplitude of ambient energies within the local structures being transferred into the Cabinet.

The next consideration is crating a support structure for the audio equipment that has rigidity, energies produced within a room can impact on a support structure, with the outcome being movement. Movement is a new energy, and this energies amplitude will be able to transfer into audio devices. Reduction of this energy type can be achieved by anchoring the Cabinet to the Wall with fastening. A decoupling device as used on the base can also be used as a separator between the Cabinet and the Wall, again to    d rIf a   

The issue with components that are situated too close to one another is EMI. I always found my system to sound much better with the amp out of the rack even if it was just sitting on the floor at least a foot away from the nearest component. Keep the power conditioner at a good distance from everything else as well.