In general, I don't think it works that way.
If you want people to install your code in a privileged position (such as a browser extension), you need to appear trustworthy.
You essentially ask your users for a credit of trust. And yes, being able to say "just read the code" is absolutely necessary, but it is not sufficient. You usually get trust by having a great track record in the past, or by cooperating with others who do have such a track record.