Explanation for parallel darlington behavior
The double-diode model for transistor is little use here.

What happens is that when you disconnect the load at Q2, there can be no collector current available for the first transistor in the darlington pair Q2, so all the current to drive must come via base terminal.

And therefore, as there must be equal voltages at the base of Q1 and Q2, the Q2 needs more base current to match the VBE drop of Q1.

This is the reason you should not parallel the bases, but have separate base resistance for each transistor, as they may have different VBE drops due to manufacturing tolerances, or different VBE drops due to the collector current.

Same thing with LEDs, you can't parallel a green and red LED with single resistor, only the red one will light up as they have different forward voltage drops.