I have a repo with only one branch (
commit 126 <-- tag v1.0
Have you ever been to a book club where members do not all use the same edition of the "book of the week"? It's a nightmare, right? Moving a tag would essentially put you in the same situation.
If you think of your repository as a book that chronicles progress in your project, you can think of a tag as a chapter heading.
Moving a tag to a different commit after sharing it is like telling all your book-club buddies
You know what, guys? The edition of the book we've all been using so far is now obsolete, because I have solely decreed that chapter 8 shall now start, not on page 126, but on page 128.
Not good. Moving a tag is a form of history rewriting, and you shouldn't rewrite history that has been shared. It's the surest way to piss your collaborators off. Besides, you write
I'm the only contributor to my repo [...]
That may be true for now, but if other people than you have access to your GitHub repository (e.g. if it's public), some of them may already have forked or cloned it (although there is a way to find out), and you run the risk of pissing them off if you rewrite history.
If you're 100% sure that you want to move that tag anyway, Git does allow you to do it. Here, you could use
git tag --force v1.0 <ID-of-commit-127>
and then you would have to force push that tag, using
git push --force --tags
But again, think twice before going ahead...