Accessibility overlaps a lot with usability, and historically web-standards + usability = accessibility.
However, there can be a few things missing, such as alt-text and making sure the keyboard focus is visible. These don’t get noticed by the majority of people, but are needed for people with particular requirements.
During the creation of HTML5 there have been several arguments around what is needed for accessibility, such as whether to make alt text required, and whether table headers are needed.
I completely understand that it’s very difficult to create an understandable, cohesive spec for HTML, so everything possible has to be done to minimise the complexity. However, accessibility is something that has to be included in such as way that developers and authors can create all their content in a way that is accessible.
For example, although complex tables are rare, it is necessary that they can be created in a way that works for everyone. Otherwise Governments and Financial institutions that have to publish content accessibly will have to go elsewhere. (Such as PDF.)
Jeremy Keith summed this up well in 2007:
I am more than a little concerned at the way that studying existing behaviour is being held up as a make-or-break point in discussions around HTML5… By their very nature, accessibility concerns are not going to affect the majority of users.
So yes, it’s useful to pave the cowpaths when you know the common ground, but sometimes you also add another path for those that need it.