You can develop websites without using prototypes.
You can also ride your bike with a flat tire. Sure, it's possible — but you don't. Your life gets easier with a well-functioning bike, and your designs will get better if you prototype.
Prototyping is essential to develop high-quality websites with a great user experience quickly and consistently.
What are prototypes?
Prototypes help you test ideas and offer clients the opportunity to give feedback early on. If you're 100 hours deep into a project, you don't want to go back and change something fundamental about your design. But when you've quickly sketched an outline for a web design and you find flaws, there's no harm done. Get out the eraser and start again.
Sketching with pencil and paper is one way to prototype, and there are many. Popular prototyping tools are Figma, Adobe XD, and Sketch. They all offer the same basic functions, so it's mostly about your own preference. My tip will always be to start sketching out rough ideas with a pencil before moving on to the big guns.
Prototyping is about making quick iterations; to keep improving.
As web services gain complexity prototyping will reamain invaluable to web designers. To prototype means you put your users first, which is always the way to go.