I'm not convinced there's anything you can do about that without losing what makes PDF such a useful format. One of the great things about a PDF is that you can drop a few pieces of paper into a scanner and end up with a PDF in seconds. That wouldn't be possible if you had to care about the underlying markup, as you do when e.g. writing html.

Adobe does have tools for creating PDFs that are accessibility-friendly, but it can take hours of work. As much as it sucks for certain audiences, it just doesn't make sense to do that in the general case.