"All Media Types" is a touchy subject when dealing with exchange tagsets. In some instances it works just as you describe, but in larger fandoms it can lead to someone offering AMT hoping for one adaptation of canon, and getting a request from someone who is expecting a different adaptation of canon. Then we have unnesscesary defaults or upset recipients.

And from what I understand about Frerin/Eowyn (I'm not familiar with Tolkien but the person helping me with tag approval is) is that while yes, they're all Tolkien and technically in the same universe, they're treated as separate by the fandom and since one would need to have read both The Hobbit and LOTR to write the pairing properly that's why it would make more sense to have it under Crossover.