Tree removal work can turn into something pretty radical when the circumstances aren't great. Most folks will want to avoid this sort of tree service unless they're sure the job is necessary. Anyone who's trying to decide should look at the situation from these four angles.
Potential to Injure People or Damage Property
One of the most important reasons to completely remove a tree is that it might fall, possibly injuring a person or damaging property. You don't want to save hundreds or thousands of dollars in the short run only to end up causing hundreds of thousands or even millions of dollars worth of damage in the long run.
Tall trees with shallow roots can represent significant risks even if they're still relatively healthy-looking. If you have a tree on your property that's tall enough to fall onto a nearby structure, ask a tree service contractor about the odds that might happen based on the species and its condition.
Holes and Stumps
It is possible you'll be able to cut the tree down to the stump and leave it there. Some folks elect to do this to avoid having to remove the roots in more radical procedures. Otherwise, they may have to deal with a large hole.
However, leaving a stump poses its own risks. It can serve as a base for insects (especially termites) to colonize the property. Termite colonies have ranges of over 200 feet so you should favor stump removal if the tree is less than that distance from a wooden structure.
A diseased tree can also pose a risk to neighboring trees. Limited tree removal can spread trees out so there is less risk. You might want to remove the weakest members of a species to reduce risks associated with tree diseases that are moving through your region.
If you're not sure which diseases are in the area, look at which trees are dying. Take photos and note the conditions of the trees. You can then check online to see which trees are suffering and what the diseases are.
Some locations will be more aesthetically pleasing once certain trees are removed. You might do this if you have a dense forest at the edge of your property and want to incorporate it into the landscape. Notably, you may need to do some stump removal if the remnants of a less aggressive process would be in the line of sight.
Click on the link for more info.