Here is the current revision of your answer:
If you also need to change the username in its directory, you may not just change it since the registry has many links to the username (though I doubt that the links are case-sensitive, you may try, but no guarantee). It might be the cleanest way to rename the current user to something else, then create a new user with the right naming, migrate all you need, and then delete the old. A lot of work of course if you have used the computer for a long time, but quite quick if it is just newly installed.
Which is just repeating what the accepted answer to that question 7 years ago suggested. While you have attempted to improve the answer, it seems you have just repeated what has already been said, in a slightly different way.
Is there a kind of rule to post only those answers which offer a solution with a needed time investment that is in good proportion with already available answers?
What you describe absolutely is not a community rule.
So that a working answer may get downvoted just because other answers are much faster?
There are many reason a user might vote for an answer. One of the many reasons to downvote an answer is a user believes the answer is not helpful. At this time it is not required, for anyone to explain, any vote they might have issued.
I got a downvote for a clearly working answer to the question "How can I change the case of a Windows 7 user name?"
I downvoted your answer because it's a "link only answer" and does not contain actual instructions. There are also numerous grammatical and spelling errors contained within that particular answer. The answer does not explain in detail how the author accomplishes what they are attempting to do. You also reference at least one question about changing your username that is specifically about Windows 10. The answer to that question is not even applicable to Windows 7.
Especially if you have a fresh system and you realize a small capitalization mistake, my answer is straightforward help. Instead of changing the username capitalization directly, you should rename your current user to some unneeded name, create a new user, switch to the new and delete the old.
You don't explain the method the author should use to accomplish that task. You reference one question about Windows 10, which describes a method that cannot be performed on a Windows 7 installation. The other link is to an answer that has already been deleted.
Even if the user did not actually want to find a solution for this, she might also just have forgotten about changing the username path as well. It should be mentioned at least. My answer thus adds value, in a very simple way, and then I ask myself why this gets downvoted.
As one of the users who downvoted your answer. I did not find your answer helpful. It contains numerous grammatical errors. It contains numerous spelling errors of common everyday words. It does not contain specific information to do what you describe, references using a method, that can only be performed on Windows 7. The only real reference link you provide, describes a method, that is only applicable to Windows 10.
When the answer contains specific information on a method that works for Windows 7, is not a link-only answer, and contains no grammatical or spelling mistakes I will revert my vote.
Very simple answer. Create a new user and delete the old. This worked for me, I bought the computer from someone else, and there were no data or programs to keep. I created a new user with admin rights and deleted the old user with admin rights afterwards. The path was changed, and the login username as well, of course.
I don't find the answer your reference in the answer you describe in this question particularly useful. It seems the only reason you submitted this answer is to promote your other answer. You also seem to have a habit of submitting low quality answers.