Search terms along with nodes

Description of the need I had someone ask me why many of their pages are inaccessible via search (they just don't show up). It turns out they are using Taxonomy Term landing pages extensively on the site, and apparently those don't show up at all in the search results.

Proposed solution Can we make the core search include both nodes and terms somehow?

Alternatives that have been considered I've started to port Term Search, but it is not ideal from an end user perspective because it requires the user to know whether they are searching for content or a term, which the typical user will have zero idea about.