Mercurial does have a few things going for it, though for most use-cases it's behind Git in almost all metrics.
I really do like the fact that it keeps a commit number counter, it's a lot easier to know if "commit 405572" is newer than "commit 405488" after all, instead of Git's "commit ea43f56" vs "commit ab446f1". (Though Git does have the describe format, which helps somewhat in this regard. E.g. "0.95b-4204-g1e97859fb" being the 4204th commit after tag 0.95b)
Rebasing updates the commit ids. It's fine. Commit IDs are only local anyway.
One thing that makes mercurial better for rebase based flows is obsolescence markers. The old version of the commits still exist after a rebases and are marked as being made obsolete by the new commits. This means somebody you've shared those old commits with isn't left in hyperspace when they fetch your new commits. There's history about what happened being shared.
You and I both clone a repo with ten changes in it. We each make a new commit. Both systems will call it commit 11. If I pull your change into my repo your 11 becomes my 12.
The sequential change IDs are only consistent locally.
No. They are not renumbered. Your 11 is always the same commit. It's consistent locally (which is what I mean by "local only") otherwise they'd change under your feet. You just can't share them with others and expect the same results. You have to use the hash for that.
No the old commit is always there, marked as obsolete with the information of what it became. No holes in history. (Assuming you use the obsolecense markers)