Are there cases in which one would not want to use a CMS? Well, yes. There are a lot of people who are opposed to using a CMS, each for varying reasons. Some of the reasons are that it then limits what you can do in terms of aesthetics, seeing as how your templates and such are set in stone and getting creative around them is difficult. There are many who question the benefits of using a template over that of having to learn to code. They seem to think that the “old” ways of using coding to get good results are the best ways, seeing as how you (the coder) are learning in the process, and the website is more flexible in what it can do and how it appears. Many others seem to think that WordPress is not secure, considering the amount of times that it has been hacked. These are all valid reasons for not wanting to use a CMS or wanting to use WordPress specifically.
Just on the basis of what I read from different developers and programmers, the main reason for their pushing against CMS programs is the lack of flexibility within one. They seem to think that the minute you are using a template that was pre-written and planned, where the coding is not your own, you have less freedom to customize it as you would like. This is true. A theme is usually someone else’s coding, and because of that it is very difficult to customize out of the realm of the controls that were given to you. So yes, it makes sense as to why you would prefer more flexibility and control in your site, especially when dealing with a client who may want something out of the box that is not available in on of the pre-written templates.
In conclusion, the realm of websites is very much an open field. There are many options and choices of what to use, and the best guidelines are your own personal capabilities and preferences. If you would prefer something pre-set and designed than a CMS is probably the best way to go. If you would prefer to have flexibility in what you design and how you design, then not using a CMS may be the better option. Essentially what it boils down to is your own capabilities and preferences. From there, the world is your stage and the internet your tutor.