As with all trends, it is important to steer clear of tunnel vision. The choice for a Headless system is not per se better than a traditional Monolith system.
To create a well-performing Headless website or web application, you will need developers with a different skillset. The architecture of the product – making the different components work together well – requires more time and attention.
A Headless solution can also mean losing functionalities that you would have out-of-the-box with all-in-one solutions. Think about a preview function for example, where you want to see from your CMS how a certain choice comes to life in the front-end. This is a standard option in almost every CMS but when you use a CMS in a Headless environment, you could lose this. In most cases, this can be fixed, but will cost extra time and therefore money.
In the end, it is not necessary for all websites or web applications to publish on multiple channels or to integrate with other systems. When you can work well with standard options to run your content- or commerce platform, it may be better to choose a SaaS solution (Shopify, Contentful and so on) or open-source solutions (Drupal, WordPress, Magento).