Bomb pumped lasers do in fact use lasing rods which produce the laser pulse before they are destroyed.
Fair enough, I was mostly trying to point out that in a bomb-pumped laser, everything happens very fast and once and you're pretty much limited to x-rays as the lifespan of each rod isn't conducive to your standard amplification and controlled release that normal lasers use. The energy in a bomb-pumped laser only makes a single pass through the rod as its primarily x-rays which cannot be reflected.
There are also reactor driven lasers
Yes, but a nuclear reactor is a lot bulkier than a bomb. Not only do you have to have the reactor and laser system, you also need coolant and radiators to keep your reactor from overheating en-route to the target. These kinds of laser would be better suited to being ship (or drone) based than on an expendable platform like a missile.
...Casaba Howitzer
While cool, Casaba's are basically direct hit weapons. They rely on plasma and plasma likes to expand stupid fast and is easily deflected by magnetic fields. They're great for propulsion, but with a range in kilometers you can measure by counting on your fingers and toes, they're not every effective standoff weapons (although good for point defense)
Also worth mentioning that if we are being realistic the focus and wavelength techs are the wrong way round, the more energetic photons would do more damge while a larger focal array should let you keep the beam focused at a greater distance
Higher wavelength photons do diverge less given the same starting diameter. But it's also harder to focus higher wavelength photons so it's easier to have better focusing tech for a weaker laser which could give it a higher range in spite of its higher divergence.