Designing and building a website, assuming you're doing more than installing a theme on WordPress, takes thought and planning from the design to final snagging.
Let's look about this in a completely arse about face manner. When building a website I use a number of off-the-shelf scripts, extensions and code to make the site look and work really well. Some of these extensions have taken developers sometimes hundreds of person hours to develop. To think I can produce the same results with a few taps of the keyboard would be misleading.
When I design a new, bespoke, website it is with my experience and knowledge of these extensions and scripts that allow me to produce the best result. I mention this because I am often asked to work with other designers. In itself not a problem, but on occasion I am presented with a finished design of which I have had no part. Of course a website can be developed with the provided design but how well will it work, has the design failed to take advantage of the technology available, how will it behave on different devices and finally will it require expensive bespoke development where there may well have been a better solution at hand?
Now that is said over the years I have worked with some excellent designers and it is really invigorating to work with other creatives who are receptive to different ideas or approaches. Of course this is a two way process, which is why it is referred to as teamwork.
In conclusion, designing and building a website has to be a collusion of skills and knowledge. It's as simple as that.