They also have tractor beams and transporters which they could easily use to clear a path for a larger ship. But they want the star in a spacesuit, so in a spacesuit she shall go.
I like the idea, and they could have even used it to help clear a little of a path for the EVA suit, but given the density of the debris field, I just don't see it happening. You have hundreds of objects coming in at different speeds, different directions, different masses and densities. I don't think phasers and tractor beams are going to do it (transporters were only used for site-to-site starting in TNG, so they would have to beam debris aboard and then back out again, not really feasible with any large masses; plus there has got to be an upper limit for mass/energy on a transportation).