In theory, yes. In practice, the typical specialist designer is going to optimize for things that come at the cost of accessibility.
But yes, in general you're absolutely right, that a good designer will take into account all factors, including accessibility. But the way that "design" has evolved in practice in means that the thing we all think of as "web design[er]" is not optimizing for it.
But yes, in general you're absolutely right, that a good designer will take into account all factors, including accessibility. But the way that "design" has evolved in practice in means that the thing we all think of as "web design[er]" is not optimizing for it.