High Power LED Circuit Design & Constant Current Source Question/Feedback
Without \$R_L\$, a much larger voltage may appear across the transistor, from collector to emitter. It is incorrect to say that the voltage at the collector is the same as the voltage at the base. The voltage at the collector will change as needed to control the current.

If the base voltage is about 2.5V then the emitter voltage will be about 1.1V. If the LEDs drop 6V altogether then the remaining voltage, \$24 - 6 - 1.1 = 16.9\text{V}\$ will appear from collector to emitter of the transistor. If 750mA is flowing through the LEDs then that much current is also flowing through the transistor, and it will be dissipating about 12.7W of power. You will need a sizeable heat sink to keep it from burning up.

There is no free lunch here. If your power supply is 24V and only 6V is across the LEDs at 750mA, then you will be wasting 13.5W somewhere. You can add a high-power resistor in series with the LEDs to reduce the power consumed by the transistor, but you are wasting 75% of your power no matter what.