A job posting for a "project leader/lead developer" will ask for "an excellent project manager, team leader and software engineer, with the skills to communicate with clients and programmers", with some some technologies and methodologies thrown in. Every full-time manager can tell you that managing complex projects or teams is an art in itself. You can spend a lifetime excelling in only that. They could equally well argue it is ridiculous to ask that someone is an excellent software engineer as well. However, they don't: it is perfectly acceptable that one should be skilled in both project management and programming. That one should have people skills and technical skills, even though each of those could be a specialization in it's own right.
The exact same holds for design. If you are offended by people look for a designer/front-end programmer, but not by people looking for a project leader/software engineer, than you are suffering from a delusion of grandeur about the importance of 'design'. There are precious few companies that can use excellent 'pure' designers. All the others are perfectly content to hire someone with adequate design skills and a set of additional adequate skills that make him useful to fulfill several roles. If that is offensive to your, you need to leave your artist-ego at the door when you go looking for a job.