Timbow0,
You are not missing anything. Changes made to a page's HTML using Firefox's Inspector are not permanent. When you reload the page, the changes are lost.
To make changes (to a page's HTML) that will persist across reloads, you will need to run a user script.
For Firefox, download and install the free add-on called Greasemonkey. That add-on will allow you to run user scripts. Then install the script I posted in this thread on May 11, 2016 ... that script will essentially change autocomplete to "on" each time
the sign on page loads.
Once you have installed the script, you may have to enter your email address once into the sign in page for Firefox to remember it. There-after, Firefox will auto-complete your email address when you type the first character into the sign-on page.
Note that in order for Firefox to "remember" your email address for auto-complete, you must NOT enable the Firefox option to clear history.
Hope this helps.