Being a web designer requires skills in many areas. You obviously need to be able to build a website using whatever tools you prefer to use. You will need to get familiar with those tools to the point that you can determine quickly whether what your client wants is possible for you to deliver.
You could take the approach of saying to your client: 'Here is a template that I think matches what your business needs and I can build you a website with your text and images in it'. Your job then becomes filling in a template with content and getting it published. However, most people with some technical skills can do that themselves online with one of the many available website builders so you are not really adding much value to the process. It's a bit like saying 'I can build a new set of furniture for you' and then bringing in a bunch of self-assembly furniture and assembling it for them!
Unlike furniture though a good website should be able to evolve. Businesses change over time and the website that is the public face of that business should be capable of evolving with the business. Your website client will want to add new features, new products or services, add announcements, reviews and many other items and as a website designer you need to be able to respond to those changing needs to provide an effective service over the longer term.
I use tools that let me design a site from the ground up so almost any layout that my client has seen, I will have a go at designing so for me it's like building a table from scratch. Just don't ask me to build you a table though!
