It is not something you want to have in your yard. While it might look okay initially, but it will eventually start to erode.
Apart from that, the primary reason removal of a tree stump is for the protection of the property. If you cut down one that is decayed, the stump still has disease. It could lead to fungi growing throughout your property, and possibly even the house.
Pests can be another source of concern. Once they bore into the soft surface of a decayed stump , they can create eggs. Your property could be infested with millions of insects.
This video explains why it’s not a good idea to delay to remove a tree or stump. If you don’t, you could end up in severe damage that takes hundreds of dollars to repair.