Look at his circuit, it has a current source.Danko Just for a moment, assume S1 (the parallel switch to D1) is the only LED he wants switched off. When you bypass D1 with S1 you change the circuit characteristics and increase the current through the rest of the LED's. Now for a moment assume he only wants D10 lit (S10 would be open). Without the 9 other voltage drops across those LED's the voltage through D10 and the associated current would be nearly a dead short to the power supply and would burn D10 out faster than you could blink.
I respect your opinions and views but I disagree with your approach. Particularly because the TS stated he might want to have all LED's out but one. I can assume there would be a circumstance where he wanted ALL the LED's off but the power supply still powered. That would be a dead short. Or at least through the one current limiting resistor (not shown in your diagram but assumed to be there) ALL the current would be going through that resistor and would get very hot if it was sufficient in size (wattage) to not burn out. But such a high wattage could potentially start a fire. This is why I disagree with your approach.
With the TS approach, each LED has its own resistor. So regardless of what state the others are in, the one that may be under consideration would be operating at the proper current. However, it occurs to me that perhaps you have a resistor at each LED and use the switch to either drop out both the resistor AND LED or just the LED only. In which case I see so many potential changes to current flow that I can't predict how the circuit would function. I suspect it would fail if the right set of switches were active/inactive. I could model it but I don't have that much time. I will model three LED's set up the way you suggest and see what numbers I come up with.