Lets do some math. A 1 Kohm resistor across a 50V voltage is Power = V*V/R, or 2.5 Watts. This is way too much heat for a component that is not designed for it, fire extinguishers optional. 10K is better, .25 Watts, but still a little warm. So you can use 100K ohm for .025 Watts (the 10 Kohm would work OK, I'm just conservative).
The more gain a transistor has, the less it loads the input, at least on a emitter follower design. Since we are trying to up the variable resistor that is being used as a voltage source feeding the transistor to reduce the resistors wattage dissipation it can source a lot less current to the transistor, because of the higher resistance. Upping the transistors gain compensates for this. Unlike most compensations, there is very little downside, many times to fix one problem you create several others when designing a circuit.
The general downside of a darlington is the increased base emitter drop, but in this case it doesn't matter. You can even use more than 2 transistors, as in a darlington triplet, for even higher gain values and it won't make much difference to this design, other than loading the adjustment resistor even less.
By the way, you can also use the emitter resistor to measure the current going to the load by measureing the voltage across it. They even make precision resistors with 4 leads in high wattage formats specifically for this function. So if you put this design in a box and spring for a meter you can have extra functionality.
The more gain a transistor has, the less it loads the input, at least on a emitter follower design. Since we are trying to up the variable resistor that is being used as a voltage source feeding the transistor to reduce the resistors wattage dissipation it can source a lot less current to the transistor, because of the higher resistance. Upping the transistors gain compensates for this. Unlike most compensations, there is very little downside, many times to fix one problem you create several others when designing a circuit.
The general downside of a darlington is the increased base emitter drop, but in this case it doesn't matter. You can even use more than 2 transistors, as in a darlington triplet, for even higher gain values and it won't make much difference to this design, other than loading the adjustment resistor even less.
By the way, you can also use the emitter resistor to measure the current going to the load by measureing the voltage across it. They even make precision resistors with 4 leads in high wattage formats specifically for this function. So if you put this design in a box and spring for a meter you can have extra functionality.