Is it fine to bunch together power wires?

You are better off having a jumbled mess than having all the cables neatly organized.

Neatly organised is good, touching is bad. My .5, 2" numbers work very well, for NOISE. As I stated..

You shouldn't tell people that.  This isn't a Cray supercomputer, where there is an actual reason for the wires being carefully jumbled as you stated... His system would CRC because it was digital. The errors were cause because of just what you stated. Field migration from HC lines within the box.  Whopper in war games... Right..

It matters very much for noise, AS I STATED. I don't care about the gobbledygook you spouted.  The magnetic field may be affected, BUT you or I can't hear the affects of it.  At 30 db or a 140 db, in my systems. Whether through XLRs, RCAs or Speaker interconnects.

I'm pretty sure, I'd be walking out on one of your installs, because of the floor noise. I said  IC running parallel. There is NO NOISE when at least 1/2" apart, and 2" with PC. If a PC cross and IC, 90 degree, right angle, again 2" apart. They will SOUND better. Typical lineman for the county, answer, typical electrician answer. 

LOL I have a family chockablock full to the top of Union electricians. Top notch men.. They all learned one day at a BBQ.. The best of the best..
They learned about Stereo gear, the ones that could still hear anyway.

They learned about cable direction, not one started out believing it, they all did before leaving.. One made up an RCA and we tested it. Sounded better one way than other.. The spool of cable was cooked on a cooker for 3 days. live and learn, they did...

Two of the 7 actually specialize in HiFi, High Current cable installs, NOW! Go figure, they alway come to Uncle Scotty with stereo questions.

Regards

No touching... anywhere. The cables DO NOT TOUCH each other anywhere.. Especially POWER CORD to Interconnect.

Take your time and rout just 1/2" apart on ICs, and PC.  When crossing the two, a  2" gap and a Right angle, (90 deg if you can).

Looks like asian dry sand ponds, rake art so to speak. All the cables look like pipe farms in refineries. Take your time, raise them off the floor. I made my own risers. Mainly to clean, and keep dust and moisture off the cable, vibration is not a big issue for me..

I use as little shielding as I can. Routing will fix it.
I do twist my PC, CW though, with double grounds, one copper one silver clad. Works better than a weave.. By following the natural twist of the wire, normally Clock Wise..

Like MC said, the CABLES gotta sound good. The routing will take care of  noise issues.. I've Never found a noisey cable, routing wouldn't take care of, unless the cable or connection was bad. It took a radio a couple of times, like I said.

I also found cables SOUND a lot better. Nothing else, just sound better, no fancy terms, no BS, just sound BETTER, behind routing... Then leave them alone... let them settle..

Regards

A lot of the times, that little noise you were hearing, and were putting up with was a routing issue.  None of the wires touch, if it's a PS it crosses at a right angle, and at least 2 inches from any IC. I have one place where this happens. Everything else can be routed, take your time. It is an art.
Grasshopper... When you can take the pebbles from my hand, you will be ready. LOL

So you know, I use active OXOs, and columns with passive subs, Lots of wire...NO NOISE. ZERO, nadda, nothing... Tube, SS, combos no noise...
Used a hand held AM FM radio to figure the really weird ones. XLR connections arching or bad solder joints, in the wire connections. I had cobwebs drive me nuts inside a passive preamp I made with an onboard LP filter. COBWEBS.. NO Noise. and no Yoko Ono.... same thing noise.

Regards