Ordering is very different to what semantic versioning is. Semantic versioning proposes that those numbers have meaning and it's important.
Whereas again, what you and I are both saying is "who cares, I want the commit".
Commit + Branch means I can answer the question "is my problem fixed (or are things broken) in the newest version of the code" - which is the actual question semantic versioning proposes to answer but can't.
Adding a release number for human readability is fine (i.e. imply some quick ordering so you can go "oh, this isn't the newest version"). But even then: when putting together systems, that's not a question I ever really find myself asking - the one I'm asking is "are these things exactly the same, and what's the latest I can upgrade to without breaking it (or conversely: which was it working fine on).
Which is why I point out the need for an immutable web at the end there: if we accept version ranges are useless for doing reliable ops work (I believe they are - i.e. you will be testing everything anyway), then in order to know anything about what does and doesn't work, I need the source code and commit logs. I probably don't want to include all of those in every release and I do want to be able to get to new versions, thus the three things I need: upstream location, upstream branch, and commit hash. Everything else is irrelevant, or sugar.
EDIT: And we can derive simple ordering numbers anyway - just count commits on the release branch since the product started. Accomplishes the same thing.
EDIT 2: It's also worth considering though, that incrementing numbers introduce subtle bias - people always want the highest number, and assume it must be better. There's always an urge to upgrade to version 2, even if version 2 might be a complete rewrite and less developed then 1 with an uncertain future. How different it might be if we only talked about branch names and commits - we're on the "beach" branch, but the company has a got a new one for the product called "forest". How different might discussions about "upgrading" be, and consideration of security fix deployment and status.