Pushing over stumps to get them out is very rare and requires a lot of weight and hp. I have a full sized backhoe and it wont do it. I have a 40,000 pound, 170hp dozer and it wont do it either. Stumps need to be dug up, and you need to be able to cut through the roots to get them out of the ground. Sometimes I have to go out as much as ten feet from a really big stump to be able to cut through it with my backhoe, but most of the time I can cut them right next to the stump. It's time consuming getting them out. If I can get one in half an hour, that would be amazing, but usually it takes quite a bit longer, depending on the species and the size of the stump.
Remember to compact the soil real good when filling the hole. Once it rains, that fill soil will absorb more water then the surrounding, undisturbed soil and it becomes mush. More then once I didn't have a big enough crown over a large hole that I dug getting out the stump and after a wet winter of storms, I found those old stumps the hard way while out mowing. They will latterly swallow your tractor if you are going too fast!!!!
One of the reasons for foundation failures on a lot of houses is there was a tree growing where the house is going to be built, They took out the trees and stump, but didn't get good compaction on the soil. Over the years, the soil settles and the foundation is no longer resting on anything. I've seen 6 inch gaps under the slab in the middle of the house when remodeling bathrooms.
Eddie