The WAI-ARIA breadcrumb example has the following rule:
The link to the current page has aria-current set to page. If the element representing the current page is not a link, aria-current is optional.
However, it was my understanding that the current page in a breadcrumb shouldn't be a link, as this link would simply take the user to the page they are already on? Is this just an oversight of the example, or is there a reasoning behind this?
There is no usability reason to have a link to the current page and from a purely user experience and accessibility perspective it serves no purpose and actually adds another tab stop and possible confusion.
However accessibility doesn't live in isolation and so we need to decide if having a link to the current page has other benefits.
Now Stack Overflow isn't the place for SEO discussion but this is something that is debated regularly as it can affect 'link juice' proportions based on the number of links on the page, I don't think there is any truth to that but that is the world of SEO for you and something you can research / consider.
The other reason is if using structured data such as schema.org breadcumbList.
Although there are ways to use structured data without a hyperlink for the last breadcrumb it just leaves the flexibility there for if using microFormats instead of JSON-LD
If it is easy enough to not use a link and change your generated 'microFormats' or 'JSON-LD' then it would be preferable to not have a hyperlink for the current page in your breadcrumbs. This would improve usability and UX.
However if you do need to have a hyperlink due to other constraints then make sure you add aria-current="page" and possibly some visually-hidden text that says it is the current page.
For example: <a href="page" aria-current="page">page name <span class="visually-hidden">(current page)</span></a>)
