Personally I doubt that being forced to design something is really being "compelled to speak", so I'm not sure I like the technical reasoning here.
Because the efficacy of the message depends entirely on your input, and it means you're forced to choose between your professional integrity (doing the best job you can possibly do, furthering your own career, etc) and your personal beliefs.
It's compelling a person to use their creative and persuasive skills to promote something they fundamentally disagree with, and the better the job they do, the more effectively the message they fundamentally disagree with gets disseminated to others.
If I were forced to use my professional skills to directly promote ideas that strongly conflicted with my most fundamental beliefs with no option to leave my job, I would wonder what kind of society this is.