The way you have suggested is actually what is done by a lot of golf courses. I would be aware of where your stump is situated though. If it is near a water source I would probably research it a little more.
Also, while the stump is rotting, you will have all kinds of unwanted diseases etc. growing in it, that you wouldn't want to spread to other plants. It probably grow mushrooms over the area at some point.
As well, while it is rotting, it is shrinking, so you would need to continue to backfill the hole it leaves for quite some time (years probably).
Hope this has helped a little. I have only removed a few trees, and I have just sawed them to ground level so that I could mow, and let nature take it's course, or they have ended up being in my garden, and I just included it in the plan.