Why is it necessary to have gear on the same phase from electrical panel?

Phase difference only applies in 3 phase circuits, houses are single phase. If you are stating one outlet is on other hot side (240 volts across both hot wires) vs both on one side (120 volts across to ground), it would not make any difference as the power supply on either configuration just converts AC to DC with the power supply capacitors storing the energy long term beyond the 60Hz.

Yes, the reasoning for keeping your system all on the same leg in your panel is to keep it separate from potentially noisy appliances, which would be on the other leg. I haven't found any benefit from that in my system, but of course YMMV.

The only thing I can think of that would improve things is to keep all the noisy stuff on one side of the panel, like refrigerator, and the cleaner stuff on the other side.

Its a myth... No such thing. IF the electrician did his job right and followed NEC as well as AHJ he balanced the 120V loads, within reason, as evenly as possibly on both Lines, legs, to the common neutral.

Also, FYI, Line 1 (L1), leg, and Line 2 (L2), leg, feed both sides of the circuit breakers in the electrical panel.

Example:

(L1) - - BRK 1 - - - - - - BRK 2 - - (L1)

(L2) - - BRK 3 - - - - - - BRK 4 - - (L2)

(L1) - - BRK 5 - - - - - - BRK 6 - - (L1)

(L2) - - BRK 7 - - - - - - BRK 8 - - (L2)

And so on down each side of the panel.

The source of power from any circuit is 120 V - therefore having some circuits on a different phase Side from the panel would seem OK.

When audio equipment is connected together by wire interconnects it is best practice to feed all 120V audio equipment, as well as video equipment, from the same Line, leg. Either from (L1) to neutral or (L2) to neutral, but not from both Lines. Example say a 120V preamp is fed from (L1) and a 120V power amp is fed from (L2) there is a 240V potential, voltage, between the two HOT conductors feeding the two pieces of equipment. With this wiring configuration there is a greater chance of noise, hum, from the system through the speakers.

When both pieces of equipment are feed from the same Line there is not any nominal difference of potential, voltage, between the Hot conductors feeding the two.

That’s the basics....

"Less than 300 microamps of ground loop current can cause hum as it flows in an unbalanced audio interconnect cable. However, harmonics of 60Hz that are generated from lighting dimmers or switch-mode power supplies sound like Buzzz mixed with a bit of Hummm and are more easily coupled by even smaller currents. Harmonics can add together when equipment is powered from different phases, so clearly there is an advantage to specifying same-phase electrical service to power the electronics systems in most cases....

Any leakage currents on the safety ground wires of split single phase load circuits fed by different phase legs will add together due to the 240V potential difference....

Power conditioners do not solve any of these common problems: Cross phase coupling (doubles hums & buzzes) .... What actually does solve them: Same phase power.
http://www.exactpower.com/elite/assets/pdfs/theTRUTH.pdf
 

(With big Monster mono Power amps the user may not have a choice and may have to feed them from both Lines. OR if money is no object a large VA rated single phase 240V to 120V isolation transformer can be used. Result one 120V Line... I worked with a member that has a single phase 240V to 120V 15KVA outdoor Pad Mount transformer that feeds a 120V only sub panel for his dedicated audio room.)

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