Any issues with bundling power cables together?

Cable management can be a problem. As long as you try to separate power and audio cables you should be okay.  Electromagnetic interference is the reason why separating cables is recommended, but if you are not experiencing undesirable noise coming out of the speakers, then there really isn't a problem, is there? Unless you just want to do it for cosmetic reasons.  I change components so often that I threw cable management out the window long ago!  I just do my best to run all the power cables to one side away from everything else and that's pretty much all. If you bundle your power cables and hear no difference, then why worry about it?

I have not tried it. Yes, cable management is a problem.

Power cords can have a big impact on the sound quality of a component. Also, the flow of electrons (the more the bigger the effect) create a magnetic field around them and electrons are effected by magnetic fields. So I would think this would not be good. This is probably one of the reasons high quality power cords make such a difference. So, it strikes me as this would have a negative impact. I always try to keep mine from running together and only have them cross at right angles when possible. Definitely not always possible.

Maybe someone has done some experiments?

The only issue in my mind is bundling noisy devices like Ethernet switches, PCs, etc. along with analog.  I use shielded power cords for my most delicate devices.

My biggest issues with respect to noise and cabling have been speaker wire close to ethernet wire or switch and speaker cable near power cords.   As long as I keep those away from each other my system is dead silent. 

I had a weird crackle noise intermittently,  mostly through the right channel.   After testing all tubes and trying others took the ethernet out of the equation and my noise went away.    I moved the switch and cabling away from my speaker cables and problem disappeared