RE "Then there is the problem of the noise being generated on the power lines"
When equipment is properly wired and grounded, there is no power lines noise for me.
RE "Even if allowed, the breaker must be designed and rated for more than one wire."
My 120V breakers from a Square D breaker panel, MADE IN THE USA, have two slots to specifically allow connection of two hot wires on a single breaker, known as double tap. Maybe cheap panel breakers don't allow but mine do.
RE "Same goes with using 14/3 and 12/3 wire for two circuits."
That mention implies the two hot wires from a double circuit cable (14/3 and 12/3) are connected to the same breaker, it is NOT the case. When a two-circuit cable is used the black and red hot wires each go to a separate breaker. Stating "Same goes..." seems incorrect. Double tapping (two hots on same breaker) and double circuit cable (each hot going to a separate breaker) are different animals.
RE (properly grounding the two circuits can be tricky)
Its not rocket science nor tricky, simply need to know how to do things when neutral and ground wires are shared with the two circuits. There's an additional safety trick most electricians and DIY don't do when installing a double circuit, i learned it from a Master Electrician, you need to put a flat head nail joining those two breakers (there's a hole for this) so that if one trips the other follows. Very logical, good reasons for this, too long to explain here. Other breakers don't have a joining nail, only those for a double circuit.
RE "or aluminum cable."
The suggested use of Alu cables is very surprising. Alu cabling for electrical work has been banned for years in many jurisdictions due to connection problems with this "soft" metal, softer than copper which is the preferred one. Moreover, Alu has a resistivity about 1.6 times that of copper. Not a great conductor.
RE "sub panel providing many more 120 volt circuits"
The many more may or may not happen since this depends on how loaded the main panel is, and the sub panel can only use the "loose" (amperes) from the main panel. An unused 220V breaker slot would provide two 110V lines.
As always consult a licenced electrician.