I don't think that yukuri could completely defoliate an area faster then the plants could grow.(In most areas anyway.) Most natural forest fires are caused by the overgrowth foliage that has died in the summer heat. If yukkuri are present in the spring time, the growth would not exceed it's limits and stay healthy even in the summer. This would be great for tree harvesters that make there living off of trees.
I'm pretty sure the average yukkuri couldn't fell any tree larger than a sapling. Strip the bark, take (very) low-hanging branches and eat seedlings? Sure.
The effort to chip away at the trunk and cause enough damage is probably beyond the attention span and strength of most yukkuris. Not to mention that when that tree falls, smashings are bound to follow.
Actually, I'm not sure if yukkuris would actually directly fell a tree, because in most stories I don't recall them directly trying to cut them down. Instead, if the various other things that do to the environment around them that might do it: cutting into it in order to suck out the sap (which for some trees leads to infection and death), destroying the soil and tearing it up, and possibly destroying the roots of trees by burrowing down.