Stuff that Japanese kids would know should be translated.
Stuff that Japanese kids wouldn't know (like Enter's French) should not be translated, because the show used those for a reason (creative or otherwise).
The simple answer is yes. Would you even translate even the person's names to the point of being hard to understand? Example "二葉さん今どこにいるんですか?" transliterated as "Futaba-san, where are you now?" now are we gonna translate it into all in all literal way like "Double leaves/ Two leaves three, where are you now?" (note: san can mean three as pronounced with this "三") stuff?. Now that would be a pure example of this trope. Now honorifics are also good to be retained due to the fact that they are useful in making us familiar with their way of addressing each other in the same manner as we western style folks use "Mr.", "Ms." and/or "Mrs." to our person addressed.
And sometimes the intended meaning can get lost especially if they are puns. Yes! Puns! Especially in tokusatsus (like that one that the Cancer Zodiarts is doing) and animes (like Bakemonogatari and Nisemonogatari). Puns are fun right?
Sorry but the simple answer is no. You seem to think that fansubs should be a way for people to learn or to teach Japanese. That is not what fan or official subs are for. They are for people to understand a show FULLY that is not in their own language.
Real translators have been doing what you have said can't be done for years and years.
I thought that after O-T's Go-Buster Oh/King fiasco people would have learned already that there are things that should never be translated at all.
Pardon me but I am not thinking that way. I am simply pointing it out that some words are better off not translated for the sake of pragmatism. I think that would somehow avoid being "macekred" by the translation process.
As an example, take the name "Boukozu Bouuzoukuu" from Carranger. The whole joke is that the latter part of the name is an incredibly lazy corruption of the former. If you leave it as is, you make them sound like more serious villains to an English speaking audience, and thus said audience is confused as to why they do some of the things they do.
However, translating it to "Bikergang Bykergang" instantly gives an English speaker the proper context for the joke and allows them to better understand what kind of villains they really are.