The problems I think of at first glance are:
You still need a really gigantic laser to move anything useful around. Why send postage stamps to other planets in a few weeks when we can send car-sized robots in a few years?
Even if you manage to get up to speed, you'll need something to slow the craft down at the destination. If it's travelling at a fraction of c that doesn't require scientific notation, that thing is probably another gigantic laser, which would be even harder to build away from Earth.
I think fusion and even fission drives are easier than this for large ships.