Words with roots from different languages
Solution 1:
The only reason would be if you're a linguist, or interested in etymology of words and such, and if you have a feeling that when creating a new word you should only use roots from a similar language. Anthropophagous and hominivorous, not anthropovorous or hominiphagous.
However, once a word is in the language and has become a new concept, the way the word was formed doesn't really matter anymore. In daily speech I doubt many people care how the word "television" was formed and that it was bad to combine a Greek root with a Latin one.
Solution 2:
Yeah, what's wrong with mixing roots? In particular, "aquaphobia" means "fear of water" if only because the monoracinate[1] "hydrophobia" means rabies.
[1] Heh-heh, I just made that up.