The whole point was that while the weapon is destroyed in the process, the nuclear blast is the "cheapest" way to create the power necessary to power such a weapon. It's lighter, and more powerful than anything else. If you can have multiple "rods" that are independently targetable (within some arc restriction, naturally), you may well get several lasers pumped out of a single device. If each device can take out, say, 4 missiles, that's not so bad a trade off.
The were used in "Brilliant Lances"/TNE as basically in lieu of a what we would consider a standard missile today.
The premise simply being that the ability to actually IMPACT another object, specifically at space speeds, is vastly more difficult than getting "something close" that can then fire and use lasers at the terminal point to "catch up" and compensate for the various accumulated errors garnered during tracking and pursuit.
Also, of course, if you can actually reliably impact something at standard space speed with something else, the warhead is mostly irrelevant -- just send slugs and make them kinetic energy kill weapons instead.
Bomb pumped lasers give you more "bang/buck" in terms of actual energy delivered to a target, again, in space, than a normal nuclear explosion. Nuclear explosions are very hot and very radiation intensive, but their real value on the ground is all that nice dense air to heat up and compress. Vacuum doesn't perpetuate the explosion as well, so the lasers help concentrate that wasted energy in to a more focused form, and thereby making them more lethal and easier to do damage with than a simple nuke. The contact range is greater (i.e. it can go off farther from the target) and more energy can be delivered.
