Or just let the user decide at the start of a private session. Firefox already does this with tracking protection. If Mozilla decides to improve tracking protection at the cost of usability (such as hiding you preferred language), than offering that as a toggle-able option on that page might be sufficient to empower the user to decide for on his own.
> offering that as a toggle-able option on that page might be sufficient
Technically speaking yes.
From a marketing/communication standpoint, I would separate this "feature" clearly from the 2 known browsing experiences. It not only clearly communicates to the user that a different browsing experience is about to start. By selling it as "the third browsing mode", it definitely also adds more perceived value to the product.
