When clearing land you have to decide if you are going to pull or cut. Of course if it is something of a large diameter or deep rooted then your only choice is to cut. I prefer to pull out brush and small trees as I do not then have to deal with stumps. However in the case of thick brush there often no grass or vegetation on the ground and if you pull out the brush you leave the ground exposed to erosion. Leaving the roots/stumps in the ground will help control the erosion until some ground cover established.
I have an area of honeysuckle bushes that is on a slope with no ground cover. If I were to pull them up it would suffer bad erosion. I plan to cut half of them out and plant some grass and when it gets established cut most of the rest out.
On the other hand areas I want to turn into garden I will try my best to pull everything out. For larger stumps I’ve seen people build a fire on top of the stump to burn it out, and that worked fairly well.