I fear your method of typing in the circumflex accent seems to work only in Microsoft Word. It does not work in Notepad nor does it work on this website. I tried typing "ê" here using your method and I was unsuccessful. I had to type alt-136.
On the other hand I do thank you for the short history of the circumflex accent. I am French but did not really know who invented the circumflex accent, and when it was introduced.