Is seeing a lab through the fog of war that big of a deal? From the gifs I would have to actively look at that area to be able to notice the visual differences. That means I don't do anything else in that time, which is a pretty high cost. It looks like the main visual difference comes from different LOD values, can't we align them, so the tree group looks basically the same when it got broken?
Regarding the breaking of tree groups on purpose: People complain about build orders being too OP all the time. We have a tool here to disrupt the enemy's build order, but this is now unwanted too? I would like to hear some more explanation why you want to get rid of this mechanic. Do you take issue with the fact that the unit doesn't need to shoot to do damage? I think it's a creative use of the game's mechanics to counter a greedy build order and it's one of the very few options when your own build order is inferior.
If we still want to lessen the impact of broken tree groups we could play with the mass adjustment for broken groups. That has already been done once and that way we don't have to introduce additional complexity, where some units arbitrarily break trees while others don't. Plus we can keep the nice visuals of a lab crushing trees while running through a forest.