Ok, i think i understand what you want.. Yes, for any given current, there is only one voltage, if the resistance doesn't change.
If LDs had an unchanging resistance, you could drive them safelly with constant voltage, and also get constant current.
But it doesn't work that way..
First of all, every diode has a different Vf. Even diodes from the same batch. If you tried to power several diodes from a constant voltage, the current would be slightly different for each of them, and you would have to tweak the series resistor, untill you adjusted it.
With constant current, the current will always be the same, regardless of small differences in Vf or even with a completelly different diode (BR or red - with CC, current will be the same).
The other thing is, that diodes don't have a fixed resistance. Their internal resistance changes with the temperature. With heat, the resistance drops. This means, that even if you select the right resistor to achieve 100mA with that particular diode, the diode will start warming up, and the current will slowly climb. More current causes more heat, more heat more current, and if you went too high, the diode can commit suicide (thermal runaway). So if you do this, you need to limit the current enough, that it will still be lower than max, even when the diode is at it's hottest.
With constant current, current is always the same, as long as the input voltage is within the drivers requirements. You can change the diode, the diode can change it's resistance, the current will stay the same.
Many people don't understand the importance of CC, and think, that they can just boost to a certain voltage, and adjust the current with a resistor. But it is actually more complicated to do safely (lots of tweaking involved) and in the end, you have to run the diode at a lower power. With CC, you can run the diode at close to it's limits, and rest assured, that it won't cross over (and start eating other diode's brains).
With constant voltage you wouldn't have to worry about the 0.5V for the FB pin. You just set the voltage with the correct resistor. But there are so many disadvantages, that it does not make sense.
If a chip can do CC, use CC. If it can't, don't use it. It's as simple as that.