It's slightly worse for EMI, since the openings allow some field to pass. How much depends on requirements, frequency, and how traces are routed underneath it. Conversely, it tends not to be a good idea where
I would guess it's for copper balance, to avoid warping the board. Copper has different expansion rate from FR-4, and copper density should match between top and bottom layers. Filling an otherwise-underutilized layer can prevent warpage.
It could also be to provide a venting path for trapped gasses; FR-4 absorbs some moisture in storage, and can blister and delaminate on rapid heating. This doesn't seem to be a precaution used much these days, but I've seen mesh planes in older boards before, maybe it used to be more of an issue.
Tim