The way we would do this, was by using REST API end-points to fetch data from Wordpress in the JSON format. While this was very simple and easy, it is also a method I dislike. For several reasons.
The fact that something can be done, does not automatically mean you should do it – there are technical considerations to keep in mind.
Wasting time with REST API
For one, communicating with REST API is done over HTTP, which means you will waste time performing these HTTP requests, and this can actually significantly slow down the loading of a website. In my experience, you often end up performing a lot of HTTP requests to fill out a HTML template, and while you can somewhat limit this by loading more data, and looping through the contents, it is still a clumsy way to make a website.
The correct way to make a site, would be to query the database directly from the server-side. At least when you are working locally. If using Wordpress, you would probably be looking at plugin and template development.
I do recognize that REST API has it uses for cross-site development, but this probably belong to a minority of cases. People might simply use REST API due to lack of knowledge or skill using server-sided technologies.
I do not like dividing developers up into front-end and back-end, because every so often, we will run into something where a broader understanding is needed. Either for optimization, security, or because of technical limitations. Designers have a tendency to desire full control over presentation, but this is usually not ideal for technical reasons, and nor is it really necessary to create a good website.
I also have the impression that many independent web-developers do not have the resources to serve their clients interests. Using REST API to quickly deliver a functional website, might just be another symptom of this. What you need to have in place, is an automated way to take regular backups, and preferably, update all of your client websites at once. How many solo web-developers have that? How many front-enders?
Benefits from using REST API
There are also obvious benefits to using REST API. Sometimes those might out-weight the downs – but, I would still highly recommend you do things properly, rather than resorting to rushing out a product.
If you are working with Wordpress as a front-end developer, REST API provides you with an easy way to fetch data from the Wordpress back-end.
The final thing I would mention, is the powerful tools available through the Wordpress platform. Using Wordpress only for the back-end, frees up your time to focus, mostly, on the front-end development of the website. This alone may be enough for some, to live with the side effects of using REST API.