I can't see how these would be bad for accessibility. The markup is a<span> with a human readable word like "home" in it.
We ought to believe someone chooses to use an icon for aesthetics AND usability reasons. If the icon can't be rendered at all, it defeats it's purpose despite it having a "description".
Ultimately, if a well designed, user-friendly system doesn't work the way it's intended to, it is an accessibility issue of some degree. Albeit, some times more trivial than others.
There are no ARIA attributes that link any of the text to the buttons.
In this example we'd add an aria-labelledby to the button which references the span with the correct info.