Have you actually tried that? If you specifically erase the center, the image does change a lot at first, but rebuilds itself eventually (albeit to a slightly different final state). It's uncanny how "biological" is feels!

I have yes.. You need to erase a larger amount of the center, but it almost always results in a collapse wheras erasing around the center typically regrows.

If you hold the eraser for a second at the center, I find that it destroys the image more often than not.