The problem is, when you did that, many websites would break in the most bizarre of ways. Even now, it still breaks a lot of the web. Couple that with a well known VPN and large swathes of the web are going to be difficult to access.
I'm sure this may go down well with the privacy crowd, but for the general user it was and still is a hard pill to swallow. I wound down any attempts, figuring a balance of privacy and usability would be better and if I were to offer this, why not just point users to use Tor instead?
I figure this is a good opportunity for Mullvad to capture its VPN users and shift them onto a platform they control. Not necessarily a good or bad thing, as I know VPN providers try to launch their own browsers and even some browser vendors launching their own VPN to capture the maximum value out of their users.