A top wish from Community-Wishlist-Survey-2022 , which (strikingly) does not yet appear to be filed in Phabricator, although I found a declined task T7388 from 2006 which asked for something very similar.

From the Wishlist proposal:

Problem: When using Special:WhatLinksHere, many of the results aren't in the body of the article, and are just from templates (especially navboxes) - this often makes finding results in the content of an article much more difficult than it needs to be.
Who would benefit: Editors (and readers) who use Special:WhatLinksHere.
Proposed solution: Special:WhatLinksHere already has (redirect) and (transclusion): add (template link), with a toggle to hide/show results that only link here from links in templates. Ideally, show the results nested in the same way that (redirect) links are - so if a template links to the article, show all articles beneath that.

Some challenges:

• The MediaWiki parser expands templates before even beginning to process links. Therefore, by the time links are processed, information on transclusions is lost.
• Is it worth recording which transcluded template is responsible for each link? This is not asked for in the wishlist proposal.
• Consideration needs to be given to what happens to links provided in parameters. For example, {{blockquote|I really only listen to, like, [[German death reggae]] and [[Halloween]] sound effects records from the 1950s. And [[Bette Midler]].}} Technically these links are being generated by the template, but editors would consider them just like ordinary links in the body of the page.
• From a data storage standpoint, a pl_type bitfield could be added to the pagelinks table. However, it is undesirable to ALTER pagelinks due to its vast size on large wikis (1.5 billion rows on enwiki) - see @tstarling's comment under Option 3 in T14019#7662302.