The settings tab needs to be opened all the time because it's there where the speech recognition happens (listen to the words and figure out the command to execute).
Technically speaking the settings tab could be closed if the speech recognition process runs in the active tab, but that will require to ask for microphone permissions every time a new website is opened, what as I see it will become in a bigger issue.
In order to have the extension turned on all the time without the need of clicking the extension icon frequently, you can pin the tab. I know that is not a solution but maybe it'll solve part of the problem.
Thanks for trying the extension and for your kind words