The advantage would be that you wouldn't need tightly controlled and hard to make materials like U-235 or Pu to make one.

I'm not in any way saying that using lasers would be a plausible route to such a weapon, since the NIF facility is huge, but if it turns out that the research needs to focus on how to get more output per shot, which I think it inevitably would since a typical conventional or nuclear power plant generates on the order of 1 GW thermal power (To match that with a 1 Hz repetition rate, likely a stretch for a MJ class laser, you would need to generate 1 GJ per shot, comparable to the energy in a ton of TNT.), it would probably be touching on areas that are highly classified.