Wizard is wizard. Sailor is background. It is not thematically appropriate for wizards to have sailing.
There are published WOTC adventures with sailor Wizards and WOTC monsters who are sailor Wizards.
It is not thematically appropriate for a battlemaster to have arcana.
Actually it IS thematically appropriate for a battlemaster to have Arcana. Just as appropriate as having Athletics in fact.
So yes, a Wizard Sailor can be thought to have sailing, but only because sailor.
Nope. And the monsters published by WOTC that are WIZARDS and sailors do not have the sailor "background"
Ahh, so spellcasting is thematically appropriate for my single class champion with no feats, racial abilities or any other way to cast so much as a cantrip or ritual, just because I've decided so?
No being an expert in spell casting is appropriate. That does not mean they can cast spells. Those are not the same things.
IRL I have a masters degree in Engineering. I am an expert in Kinematics, Aerodynamics and control theory. I can tell you more about how a raceecar works than most racecar drivers. Yet I can not drive a racecar nor am I as proficient with firearms as a professional special forces operator.
Same thing here - just because a Wizard is able to cast spells, does not mean he knows more about how they work or function.
An example from 5E: Smoekpowder is magical in the official D&D fanatasy worlds and as such a Wizard with a high Arcana would know more about how it works than the Battlemaster fighter, even though that Battlemaster can use guns effectively when the Wizard cant.
No. Theme is built into class, background, feats, etc. The player is the one who decides theme, but he is required to have the mechanics(if necessary) and/or appropriate fluff(applicable background, etc.) to achieve it, or else it isn't there.
He is required to have the mechanics and fluff as required by RAW. A Battlemaster with a 20 Intelligence who gets Arcana proficiency by switching out proficiencies from the Soldier background meets both of those criteria.
Yes he is. It doesn't not become part of the battlemaster or champion theme, though. A player cannot alter the theme of the class or subclass as it is described in the PHB. He CAN alter the theme of the character by selecting an appropriate background, like sage, though. A battlemaster sage who takes arcana is thematically appropriate, but NOT because of battlemaster.
A battlemaster Soldier who takes Arcana is thematically appropriate too. It just is.
Wrong. High bonus does not equate to "this is my thing and not yours."
The high bonus means I am better than you at it and if I say it is my thing you are stepping on my toes if you try to make it your thing and act like I should not be doing it. If you are worse than me at it, this is being an uncooperative team player.
While it is possible for me to take my +12 Persuasion and defer to your Paladin with a +6 it is not required and in a team game it makes no sense.
At no point, even if the battlemaster took sage, is it appropriate to tell the wizard to stay away from things arcane.
Not saying he should stay away, just saying he should recognize that I am better than him at it, just like if the Wizard has a 20 strength to my 16, he should be the one trying to hold open the portculis while we all scurry under it.
If it gets down to a debate on the particular arcane properties of a certain flower or the effects of a spell neither of us have ever seen or how to operate a portal, I am generally going to know more than he does about that. That is just fact and if the party wants to succeed they will defer to me on such matters.
Wizards are thematically the masters of the arcane. All else is secondary, even if appropriate via background like the battlemaster sage, even if the fighter gets a higher bonus.
There are mechanic at play in this. A non-Wizard with a higher Arcana score than a Wizard is better at being a master off the Arcane. They just are.
This is no different than my low level Wizard who rolls well is going to be much better at melee combat than my fighter who rolls poorly .... even though the Fighter is supposedly a "master" at this.
Though why the player of the fighter would antagonize another player by deliberately stepping on the toes of the wizard is beyond me. It strikes me as a pretty crappy thing to do.
I have actually played in a game from 1-20 with a Minotaur Rune Knight (another player) who crafted a headband of Intellect and take skill expert to get a freaking awesome Arcana. It was the best I have seen in play in terms of Arcana. It did not come on until medium level, but at end of game I think it was +16 and he rolled with advantage.
There were many times in that campaign where we had to make an Arcana check and it would have been foolish to let anyone else do it. He was making near impossible checks at the end of the game with party members supporting him with Guidance.
I don't know why the Wizard who did not make decisions to invest like this would think he shouldn't have been making those checks and at our table we were all happy that we had someone who could reliably make a DC25 Arcana check.
By the way, in that same campaign I played a Shaddar-Kai Fighter (Zhetilar's Finest)-Ranger (Fey Wanderer) who finished with a +26 Intimidation and +18 in Deception and Persuasion and +6 in Performance, while only having a 12 Charisma. And yes, after level 4 the party let me do every single Charisma check.
The theme is not the background, though, unless it also meets the background theme.
The rules say you can replace it with another skill. If the rules limited you to a certain set of skills fit would say so and they don't.
For instance, if you replace the sage arcana skill with investigation, something librarians and sages do, that still meets the sage theme.
And if you replace it with Stealth and Deception, it meets the Sage theme.
Sneaking around, deceiving and theft will never be thematically appropriate for sages, though.
According to RAW, they are always apprpriate for any character who already has Arcana and History.
Finally, if I am a Half-Elf Sage-Wizard I get any two skills as part of my race. If it is "thematically appropriate" for a half-Elf sage-Wizard to take any two skills, why is it not thematically appropriate for a character of a different race with the same background?
If the PC subs in stealth, he needs to write some other piece of background outside of sage to explain it
No he doesn't. There is no requirement for this, just like he does not have to write in something on how he got perception as an Elf or Intimidation if he is a Half-Orc.
This requirement is homebrew, which is fine. But it is not RAW.