Resistance losses added due to the gauge and length of wire (coax vs twisted low AWG)
Since nobody uses coax for power wiring this is rather a straw-man argument.
Power handling ability due to the gauge of wire
Which is one reason we don't use coax for power wiring.
Noise pick-up due to increases in (power supply) resistance due to (small) gauge and length of wiring
Noise is not picked up because of series resistance.
As was already pointed out, power supply circuits are among the LOWEST IMPEDANCE of all possible circuits are are virtually immune from noise pickup.
Common mode noise attenuation due to twisting of wiring
Capacitance and inductance being added due to twisting of wiring
Since power supply circuits are such low impedance (and very will filtered on top of that) twisted wiring is of no benefit.
Test Equipment Leads
Resistance losses added due to the gauge and length of wire (coax vs twisted low AWG, resistance of meter also plays role)
Test equipment has extraordinarily HIGH impedance, so at the other end of the spectrum, series resistance of the test leads has no effect on the measurement.
Noise pick-up due to length of wiring
For sensitive AC measurements (or very low-level DC measurements) we use shielded wiring (coax or even triax cable).
Common mode noise attenuation due to twisting of wiring
Capacitance and inductance being added due to twisting of wiring
As has already been observed, twisting test leads is very rare because it is rarely convenient physically, and would be improper use of the equipment.
This isn't apples vs. oranges - this is Granny Smith vs Red Delicious
It is rather more like apples vs. shoes.
Power wiring is typically extraordinarily low impedance and copiously filtered. No benefit from shielding or even twisting.
Test lead wiring is typically extraordinarily high impedance and we use proper shielding where needed for noise mitigation.