Do you speak the language of every country you visit? If I visit the main dojo of the international organization that is the Aikikai, why would I need to speak Japanese?
The thing is, you're really dealing with two different entities here. There's the Hombu Dojo, and there's the Aikido World Headquarters. The dojo is a self-contained dojo, just like any other in Japan. If you go to any dojo in Japan, it's a good idea to speak Japanese, and that includes Hombu Dojo. The international organization of which you speak merely happens to be located in the same building.
This is clear from the Aikikai homepage. Visiting Aikikai members are welcome to train in Beginner and Regular classes, but to participate in the Aikido Gakko, Women's, and Children's classes, you have to be a member of Hombu Dojo
The Aikikai is happy to have visitors from all over the world make pilgrimages to its historical main dojo, but that doesn't mean Hombu Dojo is inherently structured for an international visitors. In the end, it's just a Japanese dojo, catering to people living in Japan, specifically Tokyo.
Edit: And yes, I personally try to learn to speak a little of the language of every country I visit.