Acontent-managed site can be customized

Good question. The best answer is that it all depends on your project's specifications. Here are a few scenarios where a custom CMS would make sense:

You have security concerns or corporate security requirements that would make off-the-shelf platforms unacceptable. An example of this could be stringent security requirements that limit the amount of software licenses allowed, or that require tightening so severe that it would inhibit the ability of the platform to operate correctly. Also, remember that off-the-shelf platforms are more susceptible to random attacks by bots and other automated attackers.

You require advanced features. If you plan on having a website requiring advanced customization, evaluate if you are pushing the limits of off-the-shelf CMS platforms. An example would be software that is core to your business that must be custom built on top of the CMS platform. Future risks could be the inability to run a proper software update, or even worse, a software update breaking your custom code. It happens all the time!