You've really combined two different topics here...easier content management vs. easier site management.
The short answer is, yes, CMS software does make content management easier.
The long answer...
CMS software is intended to make only content management easier, and it's intent is not to manage your website or server security. The truth is, your website or server can get hacked with or without additional software in place, and the difference between having or using a CMS application has no bearing.
The fact is, there is more than just content management, when considering starting and managing a website. There is content, design, design consistancy, SEO, site & server security, usability, network stability, etc. A CMS application takes care of 3 of those things, content, design consistancy, and usability. Essentially, these would be 3 things you no longer have to worry about.
In a sense, you can compare your opinion to the purchase and use of a new PC. A computer was created to make daily tasks, communication, etc easier. However, now that you have one, you can't simply use it, you have to make sure your antivirus software, anti-spyware, anti-adware, Operating system, additional 3rd party software, browser, etc is up to date. So the time that a computer saved you on your daily tasks and communication, is now taken up by keeping your computer safe from threat.
The fact is, there is a certain level of responsibility of the user that accompanies any purchase of any item. The item may be created to make a certain task easier, but it becomes your responsibility to make sure it continues functioning properly, through proper care of the item, and proper maintenance.