So, general things I've learned from comments are it's competitive for sure. Small businesses don't care much about how good a website looks. There is less demand for web design and more agencies and people to fill that demand. A website doesn't make such a big impact on users, so they won't pay as much or care as much about it.
So, it's becoming clearer that I should not start web design. But this discussion is not over. I want to understand the creative business more, so feel free to share your thoughts on parts of the creative world which are high in demand but low in feeling that demand.