My understanding is that cookies etc aren't shared between containers, so I can stay logged in, and not be tracked across websites.
If it's achievable, why compromise?
This is a surprisingly effective one when combined with other users of your network. A couple of years ago, I started getting Facebook ads for things I'd never looked at, but that I knew my wife had looked at. We don't share any devices, and she doesn't even have a Facebook account.
It's pretty troubling how invasive shadow profiles are.
Some people just want to pick a different point on the tradeoff between convenience and privacy.
Imagine User A uses Fastmail every day, logging in manually every morning. User B uses Fastmail every day, with a saved login cookie. How is User B's privacy any worse? What would User B gain from not having that choice?
User B's privacy is objectively lessened by allowing tracking cookies, but that is their choice. What is out of the user's control is what mullvad chooses to spend their time supporting.
If mullvad allows users to turn off a privacy feature, now that's a permutation they have to test for. It's also an attack vector they've enabled, either through user carelessness or social engineering. Mullvad wants to be able to say "here's a browser, it's 100% private" and not have to say "as long as you do X, and don't do Y, and...". Every other browser already does that.