Sure you can, you can write HTML that does things that a WYSIWYG editor can't. Additionally, you can debug bad markup when it occurs.
You've discovered the challenges in staying competitive in the era of good WYSIWYG editors. Your edge is in dynamic HTML programming. I can assure you that my company definitely has a need for people who know HTML, as we rarely create a new page from scratch but usually just modify existing content to add new features.
PS. Your tale reminds me of the short story "Profession" by Isaac Asimov*, in which the protagonist is part of a society that educates everyone through the use of tapes. Except he is an unusual and very special individual, where he gets to write the tapes. Who is going to write the next generation of DreamWeaver, or write webpages using the next generation of HTML that the WYSIWYG editors do not support? That would be you. So I'd suggest you learn more programming - javascript, PHP perhaps, and branch out beyond strictly web design. Leave that to the Dreamweaver monkeys like your friend. You are capable of so much more!
*The text is available online, but I shall not link it as it would be a copyright breach.