As an avid backpacker who has been on just about every trail in the southern Sierras, I have over the years seen instances where certain lakes and campgrounds have become so overused that every tree has been stripped of anything brunable, all the downed wood has been burned, you can't dig a hole to do your job without finding the "surprise" of someone else's job, etc., etc. When it gets to this point (hopefully before it does), the Forest Service closes the area for several years to allow it to return to nature.
The above to illustrate that they (the FS) will do it. And if they do, it will probably be because it is needed. So do be careful, do pack out your trash, do dig a hole for your job (and your dog's job) so that the place doesn't look trampled to death. Leaving Deep Creek as "natural" looking and as devoid of human impact as possible will be the best insurance against closure.