It is my strongly held belief that every web designer or developer should know something about accessibility. However, this has its limits. For instance, I would expect that a good designer would know that images should have alt attributes or that headings are important. But I would not expect them to know how to debug an issue with ARIA using a screen reader or how to fully test a site for accessibility. I wish it were otherwise, but experience has shown that this is unlikely.
If you want to create a site that is at all dynamic, and you want it to be usable by the widest audience possible, then you probably need an Accessibility Consultant.
I have helped out on a variety of accessibility projects, and my level of involvement has varied anywhere from closely reviewing each page multiple times throughout the development process to simply answering a few specific questions about what works, what doesn’t, or how to make X usable by keyboard-only users. My site reviews can vary from a close inspection of the code, to simply checking the site in a browser with a screen reader. It all depends on the clients needs and the sites complexity.
What I don’t typically do (unless the client insists) is modify the project files directly. My thinking is that the designer/developer knows the code better than I do, and she can make the fixes in much less time. Also, if she makes the changes herself, then she probably doesn’t need to call me the next time the same issue comes up. I prefer the role of teacher to that of developer, though I’ve done both.
Accessibility is not an impenetrable art. It’s just a matter of understanding the various factors and having a little experience.
If you are interested in my services, contact me and we can discuss your project specifics.