Not to mention the money they would save on electricity bills.

That's not the purpose of the research, though. They are solely focusing on the energy transfer between the lasers themselves, and the output from the reaction. It's not clear that higher energies or bigger targets will teach us anything new.

Upgrading the lasers would slow the project down as new hardware is installed and issues are worked out. Not to mention I doubt the new hardware is cheap, and may be more expensive than burning excess energy using old laser tech in the meantime.

Other research groups work on laser efficiency, and the "final product" using this method (if it ever proves viable) would put together all the best pieces to get the best efficiencies.