Removing a tree doesn't necessarily mean removing the stump, and people are often surprised to learn that. Sometimes people want to remove the bulk of the tree but aren't concerned about digging up the stump, or they want to save money, so they get rid of the part of the tree that's caused a problem. However, it's a good idea to get rid of the stump too for a number of reasons if you're removing the tree. That means you need to find a tree service that will remove both the bulk of the tree and the stump at the same time.
Stumps Can Sprout and Spread Disease
If you're removing a tree because it was diseased, the stump likely has those same pathogens in it. The stump can spread the pathogens to nearby shrubs and trees (depending on the pathogen, of course), and if the stump is still alive, it can resprout. While the sprout might remain tiny for a long time, it will look odd, and you'll have this stump in the ground that is not serving any purpose other than to remind you of the tree you just got rid of. Instead of letting a diseased stump fester and adversely affect your yard, have the stump taken out at the same time. Remember, though, if you're removing it because of disease or pests, do not keep the stump grindings.
Why Wait if You Know You'll Need to Remove It?
Even if the stump isn't harbouring pathogens or pests, it's not doing anything other than being in your way. So, removing it is the best option, and if you know you need to remove it, why wait? Why take the tree but leave the stump for another few weeks? Assuming you have the money to pay for stump removal, you may as well have it removed along with the rest of the tree. If you don't have the money for stump removal, talk to the tree service; they may have payment plans or financing – or they could offer bundled services (e.g., tree removal and stump removal done at the same time) for a lower total price that turns out to be affordable for you.
Get a Head Start on the Rest of Your Landscaping Plans
If you're removing trees, no doubt you have plans for your yard once that work is done. Leaving the stump in place for a while does nothing except delay your ability to start work on the rest of your landscaping plans. Yes, you could work on other parts of your yard, but leaving the stump there for a while doesn't help matters. It can interfere with machinery you're trying to bring in to work on the yard, too.
When you arrange for tree removal, ask the tree service about stump removal, too. Find a company that offers both, and arrange to have the stump removed at the same time as the rest of the tree. You'll feel a lot better knowing that all of that disruptive work has been finished.