Are you ready to give up control, and how much?
With a CMS, you are committing to a system that has limits and your content has to fit into the confines of those limits.  When you incorporate your website into a CMS, you give up a certain amount of control and no matter what CMS you choose a developer will be needed for custom work, which is what you wanted to get away from by using a CMS. 

How frequently do you need to update content?
You might need a system that lets you add new entries easily if your site is mainly about content like videos, blog posts, and press releases but a CMS might not be needed for a site, that deals with simple content. A good example is a pricelist that changes once or twice a year. A Content Management System would be overkill and what you really need is a good web designer and a basic HTML web site.

Have you planned for the costs up-front?
There are plenty of Content Management Systems to choose from but to incorporate a site into a CMS, you have to spend money. And changes to your content adds extra time to the project. And don't rule out the cost of a beefier webserver to handle the CMS. Many content systems need more disk space, memory, and extra server features. A cms-less HTML website can be run on many cheaper servers without the added expense of a larger system.

Are you ready for the upkeep and maintenance you are going to need?
Management systems ALWAYS need to be maintained. With open-source content management systems (WordPress, Drupal, Joomla, etc) there is a constant rush of hackers trying to access your site. This is why many content management systems are updated frequently, sometimes daily, to respond to the growing number of problems, issue fixes and help keep their sites secure. An out of date CMS is a high-security risk and can lead to problems down the road. And if you have more than one site on your server you run the risk of neighbor sites being infected or hacked. You also run the risk of being blacklisted, infecting your visitors and being dropped in SEO rankings. 

Keeping your CMS up to date makes that harder but it is going to cost you either time, money or both. In the end, you will need to either pay a web designer or learn to maintain the site yourself.

A CMS might not be useful if….
You don't need to use a lot of multiple languages and localization.
Your customers and clients are regional and a brochure site is all that is necessary.
You don't have a need for content like press releases, blogs, and etc.
You post relevant content to social media like Facebook, Twitter, Instagram and more.
Your content seldom changes. An HTML site is would be a better fit.