Stop in for a cup of coffee

Neighbors did that all in their front yard, have a nice lawn over it. One thing they have to deal with though is that they get sinking/low spots where the root balls were as things break down and they have to add dirt and replant the grass almost every year. But they are going for the golf course look, doubt I'd do what they are doing.
That's why I just cut, dig, and bury them a few inches below surface level and leave the ball in the ground.