Regardless of who one gets a Dedicated Server from and whether it is Managed or not, there is the fact that running a Server requires certain basic knowledge, by the person who responsible for it. Knowing how do things yourself is always to your benefit -- faster too.
The basics would include things like; familiarity with working in Shell, restarting or stopping Services, making changes to the httpd.conf file, minor troubleshooting, etc. It goes without saying that the time required for operating & maintaining a Server will increase whatever workload one currently has. There is also the time required for learning -- there are always new things to learn and understand.
Responsibility is the big thing. A good ServerAdmin will always keep this thought in the back of their mind:
If I make a change and it screws up the Server, how long will take to fix it?
If the ServerAdmin cannot fix it, they go to their DC for help. That alone means it's going to take longer and there may be an additional cost involved. Money will not be an option either, because a Server that is down needs to be brought back up ASAP. If one is responsible about operating their own Server, they make sure they either have the time & knowledge to do it themselves, the money to pay someone else for it, or both.
I'm not trying to scare anyone away from running their own Server, just pointing out a few basics that need to be considered beforehand.
