A friend asked recently about whether it would be a good idea to move their company domain to the same discount hosting they use for their personal website. My reply was that it was fine to move the hosting of the website but that it was a bad idea to move the domain registration to the same place that hosted the site.
"Can we leave the domain registration at the registrar and still move the hosting? And why is it bad to move the domain registration to the hosting company?" was the response.
The bottom line is you should never, ever, absolutely never, have your domain hosted with the same company that is the registrar for your domain. If you have this today go change it now and then come back to read why you got lucky.
Two centuries ago when the revolutionaries were making themselves into founding fathers of the United States they had the concept that one should keep power and responsibility divided amongst different branches of government. This serves several purposes including making sure that one bad apple doesn't ruin the batch. Even a collection of bad apples need to get the consent of plenty of other actors before they can ruin the batch.
If you haven't already had an experience along these lines you almost certainly will some day. You'll wake up and find that either your hosting company or your registrar is offline. If you're lucky it's a temporary thing. However, Murphy has a law about this which suggests that the time it will happen is when you can least afford for it to go south. The reasons for this failure are so varied they are hard to imagine. From a registrar going off the rails to a hosting company ending up upside down or even a dispute with the hosting company over the fees, and on and on.
When this day comes if your domain registrar and your host are one and the same you have very few options. This is doubly true if your email is hosted with the same hosting provider. Imagine for a moment what happens when something goes wrong: You suddenly need to transfer your domain which, if things are working well, involves sending some emails back and forth. Of course if your email is unavailable this gets significantly more complex. What would have been a hours to days task grows into a weeks-long task in many cases.
Having been down the road of having a host who could manipulate domain records it is just plain no fun. Find a registrar you like and a host you like and use both, as long as they aren't one and the same.