This is not some bizarre idea - Lawrence Livermore is officially a part of the DoE's research into maintaining and improving thermonuclear weapons. That there are some vaguely imaginable applications in energy generation is at the very best a bonus.

Remember that each shot of the lasers also destroys 10 million dollars or so of the highly precision engineered "housing" for the fuel pellet (called a hohlraum).

The lasers don't directly hit the pellet - they hit the metal walls of this hohlraum, causing it to grow so hot that it emits x-rays, and its shape is perfectly aligned so that those pellets hit the two sides of the pellet at exactly the same time, causing two "ripples" to compress it so much that they force the atoms to fuse in the middle and produce a chain reaction that has to consume the entire amount of fuel before the force of the implosion dissipates, at which time all of the matter violently explodes. The brunt of that explosion (and the neutron bombardment from the fusion process) is taken up by the hohlraum, which is ireedemably destroyed and can only be, at best, melted down as raw material for the next hohlraum.

Edit: tldr, this is exactly as useful for energy generation as an internal combustion engine whose pistons are destroyed every time the fuel ignites.