Hi Petyay,
1. This is not entirely true, inject.js and all open sites did't include Google Analytics,
Google Analytics includes only in TS Menu(popup.html) and background.js:
And only one case when data can arrive to Google Analytics from site pages - is Javascript Error on inject.js - in this only case stack trace and error message will be sent to background.js and then sent to Google Analytics.
2. This is a good idea to add Google Analytics - optional on configure page.
Will be added in next release.