The only authentic way to translate Mad Dog Princess that is exactly as the author wrote it is this: 狂犬姫.
Authenticity spectrum, from most authentic and literal, to least literal.
Step 0: 狂犬姫 - Drawbacks: Most people here can't read what this says.
Step 1: Kyouken Hime (TL note: Hime means princess and keikaku means plan) - Drawbacks: What are japanese words doing in my fantasy series set in a western-style-world? Also, We've already lost the understanding the kanji gives readers who know Japanese.
Step 2: Mad Dog Princess - Drawbacks: Sure, I guess it's what the kanji means, but how can we be sure that mad dog means the same thing in both language? Where I'm from, mad dogs are poor dogs that got infected by rabies and may need to be put down.
Step 2.5: Rabid Princess - Drawbacks: Not sure if this isn't more literal, given the usual context you see the characters 狂犬 in.
Step 3: Berserk Princess - Drawbacks: I guess it's no longer what the kanji literal means. At least it sounds pretty cool to me, and conveys the same princess. Maybe we could use the word berserker?
Step ???: Crazy-bitch princess who you shouldn't f*$! with cuz she's a crazy-bitch princess - Drawbacks: Uhh... too long. Not even sure if it got the nuance right. Go back!
Note: the spectrum may not necessarily be 1-dimensional as portrayed here, because nothing is one-dimensional. Not even bland waifu #4 from generic harem anime #3.
Anything past step 0 has the translator making choices on translation and changing what the author wrote. Localization vs Literalism is a slidey scale, and I guess TLers are free to choose where they put the slider.
The argument against using "berserk" because it literally means "mad dog" would be the same argument against using "kyle" because it literally says "Kairu".
"But that's what the author intended," one might argue, "Kyle is obviously the name the author intended to write! That conveys the same nuance!"
That in itself is a judgement on what the author meant. Sure, Kyle isn't too far up the localization spectrum, but you could make similar choices about honorifics like "-sama" (No english speaker uses -sama, and obviously Kairu-sama means Prince Kyle!)
They're choices. And if the goal is for an entertaining experience for leechers like me, then it doesn't actually matter what the choice is, as long as the target audience understands it. Whether that target audience has newbies who've never read another mad dog manga, or someone who does know what every honorific they see means, is up to the TLer.
Relativism: The way to argue without actually coming to an agreement, since everything is relative and nothing is absolute.