An older but still relevant post by Evert Pot on why and how you should also test your packages with the lowest versions of it's dependencies.

In some projects, there may be packages lying around that are not the latest version. This could be because it introduced some BC break, or introduced a bug. If other packages also use the package that’s being held back, they may get an older version as a dependency. So for package maintainers, they will want to find out if their package correctly works with the oldest package they claim to support.

https://evertpot.com/testing-composer-prefer-lowest/

EDIT: Here's another old, but also still relevant, blogpost on the subject by Cees-Jan Kiewiet:

https://blog.wyrihaximus.net/2015/06/test-lowest-current-and-highest-possible-on-travis/