I can see that.Wouldn't that mean something completely different? If I'm English and I immerse myself in Icelandic culture, my English culture is then excluded from the equation. I'm trying to experience Icelandic culture as well as I can, and temporarily ignoring/suppressing my own culture to the best of my ability.
However, there are lots of fun moments when two or more cultures meet on a more equal footing. Mixing cultures is quite a different thing to immersing yourself. If you're a young person travelling abroad, you'll likely meet fellow travellers as well as locals, and get into situations where you've got a German, an Israeli, a Brazilian and an Australian all having a drink together. That's not cultural immersion, that's multicultural fun, or cultural mixing.
It depends what OP really means.