Web developers will continue to exist 10 years from now, but they must adapt to a new technological landscape. Providing a personalized approach to optimizing the mobile interface and other devices and e-commerce will be even more important than now. The future of web design in the face of this suggests that, as a discipline, front-end development is far from dying, and job prospects for those who want to enter the field still seem strong. When I first started developing websites, the notion of responsive websites was relatively new and most companies didn't use cloud computing platforms like Amazon AWS.
Ten years ago, much of this would have been done by back-end developers, since most of the application logic was managed on the server. Without code, designers who were previously only responsible for creating the image of a user interface can now take charge of front-end development on their own. Front-end development will continue to consist of developing user interfaces, but they won't necessarily be graphical. The increasing complexity of front-end development has produced a kind of division within the field; you can now find people with the same position, but with very different approaches and skills.
And the growing technical needs of many industries indicate that front-end development is still in high demand.