Yes - controlling it by voltage doesn't work if the regulation span is almost non-existant, and moves with temperature.

That is why the design must have a component that reduces the voltage over the LED/laser when the current is increasing, and increases the voltage when the current is decreases. A standard series resistor manages that, as long as the input voltage is reasonably well known, and the voltage over the resistor is large enough. A constant-current generator will work for a much wider range of input voltages and can also be made to work with a very low drop-out voltage.

A diode in series with a LED or laser can only adjust the voltage very little with changed current. So either the laser will get too little voltage, or the laser will get enough voltage to go up in smoke.