FWIW, the CheckUser-UserInfoCard feature will also show the count of current and former blocks affecting a user.

I think those users may simply want to go to Special:BlockList/<USER>. I don't see any benefit in introducing permission-related complexities.
Perhaps we could just add a tool link to the special page on Special:Contributions, right after the talk link in non-admin view, where the manage blocks link is shown in admin view.

But Special:BlockList does not display former blocks.

Speaking with my volunteer admin hat on

Even though ordinary users cannot modify blocks, there are no reason that only sysops can view it.

I would argue that:

• Letting non-admins see the page goes against the standard for most special pages, where the user viewing the special page should have the needed rights to execute the form on the page
  • For example, Special:Block would then be listed as "Block user" on Special:SpecialPages for all users which I would argue could be confusing (i.e. a non-admin wonders why they can see a special page that is labelled as blocking users)
• The special page is often customised and/or built with the assumption that only users who can block can see the page
  • For example, the list of active blocks have action buttons in the Multiblocks interface that would need to be hidden
  • The blockiptext message assumes the user has the rights to block and is often customised on-wiki to add more information specific only to admins (e.g. https://en.wikipedia.org/wiki/MediaWiki:Blockiptext)

But Special:BlockList does not display former blocks.

Sure, though I would argue it would be better to add the former blocks to this page if the user enters a specific target.

Furthermore, Special:Log/block will allow you to see the information (though probably less structured) and CheckUser-UserInfoCard displays this information too

Letting non-admins see the page goes against the standard for most special pages, where the user viewing the special page should have the needed rights to execute the form on the page

Cf: T376378: Allow non-admins to use Nuke's page listing feature for a case similar to this task. And also T27319: Make Special:UserRights available to everyone.

For example, Special:Block would then be listed as "Block user" on Special:SpecialPages

"Manage blocks" would be a better term (which is how MediaWiki.org help page named).