Almost all localization of the websites comes from localization resources (the exceptions are help pages, tags and other content which is stored in the database instead of being produced by the engine). Translating badges would require creating a custom set of localized resources for a website.
While it's technically possible, it's probably too much pain with little gain. A lof of customization options were cut during the style update some time ago to make maintaining and upgrading sites easier. Translating badges would mean going in the opposite direction.
Maintaining localization on international websites is a huge pain already as strings are constantly added, changed and removed. This requires coordinated work of volunteers and employees. This is unlikely to be supported on a random website "just for fun".
You also need to consider another factor: mixing languages is often a bad idea. I always try to keep content and UI in the same language on all websites. It's harder to read content and navigate a website if I have to constantly switch between languages. The less switching, the better.
Ideally, there would be two websites for each language: for language learners and for native speakers. The first would have English UI and English content, the latter would have native UI and native content. This is the case for Russian which has "russian" and "rus" websites, and English which has "english" and "ell", but not for Spanish which has only "spanish" website. There's zero consistency and logic behind this, which makes the whole system a mess, and translating a random part of a website would make it even messier.