The general recommendation in the privacy communities is that if you want to achieve maximum privacy without using Tor, your best bet is to use Mullvad Browser for your general, everyday browsing because it is the only browser besides Tor that can combat against advanced fingerprinting, while offering a great, ephemeral browsing experience. Then, you could use something like Brave or hardened Firefox for the sites where you need to log in. While this setup may not work for everyone, it is still very much recommended.
So, I would say that Mullvad Browser can definitely be used as your default browser, and it is even recommended. The use case that you’re describing for Mullvad Browser seems closer to Tor for me, because most people don’t use Tor all the time or even for all of their general browsing, and instead use it for only something very specific, since Tor has many usability trade-offs that would make it a pain to use for most of your browsing. On the other hand, while Mullvad Browser also has some trade-offs, such as the default private mode, they shouldn’t matter in a use case, where you only use Mullvad Browser for your general browsing and don’t log into your accounts.