I've never used Mercurial, but a simple one based on the explanations and my experience with Git:

Locating the branch a commit originated from. If a git branch has been merged into (or rebased on) main or another branch, there's no way to tell which commit came from which branch. But sometimes I'd really like that information to figure out what prompted a certain change. Without it, I need to use external tools like a ticketing system and hope the other developers added in the necessary information.

Most of the time you're right, it's little more than a detail, but sometimes I miss the querying that it allowed. You could ask for things like a list of all branches that branched from a specific parent branch and modified a specific file, Which can be handy when you want to understand the impact a change might have before you make it and try merging.

Having the branch name embedded in the commit means you can meaningfully ask this sort of question. In git's model you can't say a changeset is in a specific branch once there are child branches further downstream because the changeset is in all of those branches.

Rather than come up with lots of examples for other queries (I know it wasn't the focus of your question, but I think it's really neat), I found this page which seems like a reasonable description.

If I hand you a commit, you cannot tell which ‘branch’ it is on without searching the git history and hoping that you only get one answer. That’s a bummer if, for instance, you’re a github action and only get handed the commit. If it’s on the master branch, I want to do different things than if it’s a dev branch.