+1 on Mike's explanation. The LD acts as a load in this circuit. When you are supplying regulated current and unregulated voltage, the diode takes what it needs to lase and the rest is dissipated into ambient heat (out into the environment -- useless). With the circuit that I have made, I tried to keep the voltage a little higher than what is needed for the worst case scenario.
Now, when you regulate voltage as you suggest... here is what happens. You have obviously seen pictures of the inside of a laser diode. It is a VERY thin wire that connects the diode leads to the lasing dye. If the wire is at room temperature then it would have a MUCH higher resistance than it would at, say, 70 Degrees Celsius. 70 degrees Celsius is a very common temperature inside a diode... INSIDE, not outside. You have to take everything into account now. With the wire getting hot, the resistance is EXPONENTIALLY dropping... lower resistance means higher current. The more current there is going through a tiny wire, the more heat is being generated... it's a domino effect that you CANNOT stop if the current is not regulated.
I say it again... Unregulated current into a diode of any kind, LED or LD, is just a death wish. When using the LM317 as a voltage regulator the current is capped at 1.5 Amps on average... 1.5A will fry a 500mW CW diode! These are rated 80mW CW. You can do the math now...
Current is not a function of voltage in these situations, it's only a function of the load, which is a variable. When you control the current, the variable is the voltage. With a 6V supply, even if the voltage jumps up to 6V all the way, the diode will be fine. But when letting the amps fly through uncontrolled by anything other than the laser diode, the voltage you supply is nothing but what voltage you want to fry the LD at... ;D Try and connect a DMM to your 2 x CR123A setup and check out how much current you get through... depending on your batteries and DMM, they might kill your DMM!!
I believe you have the choice to do as you please. I am simply doing everyone else a favor here by trying to keep their LD's alive. Please, by all means, if you feel that that is how you want to run your LD, that is ok. But advising people to do it is not very nice. It is simply a matter of luck that is keeping that diode alive for as long as it stays alive, and I'm sorry to say that...
GL all, and be safe;
DDL