I'd put it like this: If you want to run something more than just a run-of-the-mill dungeoneering campaign with stereotype characters with just some weird names for gods and places slapped on 'em, each Player Character should be a 'hero' as people understood them in those times.
While that's one way to approach it, keep in mind that our records from those periods are very sparse. Even then, we do have records that paint a far more mundane view of things. As some of those who have looked at Mycenaean Greece have put it, for example, in the Illiad and Odyssey you get the impression of kings spending all of their time doing cool things but when you dig through the tablet archives from Pylos, they look an awful lot like bureaucrats who spent a lot of their time keeping records and collecting taxes. The records of battles you'll find on the walls of Egyptian temples can differ from what the diplomatic exchanges suggest because they contain a fair amount of propaganda.
So the unasked question here is whether you want a realistic Bronze Age or a heroic Bronze Age or a mythical Bronze Age and to what degree. It's like saying you want to run a game set in the 1920s. Is that the real 1920s, a somewhat stylized and mystical 1920s, or pulp 1920s? There isn't just one way to approach the period and not everyone is going to prefer the same option. To be perfectly honest, the Glorantha-style "mythic" approach to the Bronze Age doesn't interest me at all.
That is, the hero can be a king, a king's buddy, nobleman, warrior, tribal chief or whatever.
I don't see any reason to limit the setting like that, any more than a game set in the 20th Century should limit characters to movie stars, musicians, politicians, athletes, and wealthy businessmen because that's what appears on the covers of magazines. Gangbusters, Call of Cthulhu, and Spirit of the Century are all games set in the 1920s and I think it would be silly to claim that only one of them is the right way to play in that period.
Sure, you
can approach any period from a heroic and mythic perspective and plenty of role-playing games do, but you don't have to and plenty of games don't.
Playing the crew of a ship like those found at Cape Gelidonya or Uluburun could be interesting in a Traveller sort of way. Playing the spies like those who infiltrated Jericho with the help of a prostitute for Joshua could be a lot of fun. Playing the guards for the merchants who travelled from Mesopotamia to Harappa by land or by sea could be interesting, the classic "caravan guard" adventure. And one doesn't necessarily need to be the "king's buddy" to be an agent of the king on a diplomatic or trading mission. In fact, Harry Turtledove's
Between the Rivers isn't about a Mesopotamian hero, but still has magical and mythical elements.
They are never thieves, in the sense that they covertly take stuff from other people who belong to their own 'in-group' (that is, family, village, tribe, city, kingdom, or friendly strangers, 'guest-friends').
And such characters are rarely really "heroes" in the same sense that most other figures are, either, in any other period or genre. In fact, many of the dark comic and pulp heroes are, more accurately, "
antiheroes". There is no reason why one could not play an antihero in the Bronze Age.
However...a hero can take, with force and possibly involving some guile, anything – women, cattle, treasure – from enemies and foreigners. To seize with force, to kill – it's cool, it's honorable, it's what heroes do.
So you think a hero would never hide in a wooden horse and kill their tricked enemies in the night and murder their children when they are unprepared? Again, the question is how you want to play it. Could a game of Egyptian tomb raiders be a blast? Absolutely, even if the prevailing political culture of the time considered them vile scum. Could a game of Mesopotamian temple robbers be fun? Absolutely. You could even run games stealing liberally from Hercules, Xena, and the Scorpion King movies as inspiration.
(Of course, the victims might disagree, judging by ancient complaints about thieving Amorite nomads etc.)
Absolutely. The "heroes" of the Illiad and Odyssey were thieves, narcissists, rapists, and murderers who slaughtered the Trojans caught off guard by trickery. Heroes? How about Ramesses II, who was pretty much a hero in his own propaganda for not getting his butt kicked after being ambushed at Kadesh by the Hittites? If you want a more modern example, compare history's view of George Washington, who slipped across the Deleware River to ambush the Hessians on Christmas Eve when they weren't prepared?
Again, this goes back to what sort of reality do you want to depict in a game set in that period.
The 'sneaky thief' did probably exist, but was considered vermin – and treated as such.
Same with tomb-robbers, if found out.
Of course, tomb-robbing did happen quite a lot, especially in Egypt where they had the smart idea of burying large amounts of valuables with the dead. Tomb-robbing has been referred to in some contexts as a kind of local 'cottage industry'. The point is: you don't boast having found things in some underground tomb or complex; it is an impious act and 'certainly to be punished by the Gods' (well, in theory, that is; in a Mythic Mesopotamian Campaign, I suppose you'll get bad dreams and have your limbs rot off your body...I have visions of entire villages of tomb-robbers with various nasty disfiguring diseases...). In Egypt, when caught, they would insert a sharpened piece of wood into the business end of your digestive tract (of course, any bigwigs involved, like a prominent high priest, might escape punishment. Plus ça change...)
And how is this different from how things work in a typical D&D game? Do they normally give thieves -- uh -- rogues a pat on the back and a key to the city when they are caught picking the pocket of a wealthy merchant or raiding the palace of a king? In the movie Conan the Barbarian, do Rexor or Thulsa Doom invite Conan in for tea after he raided their temples?
There's a nice episode in the TV documentary series 'Ancient Egyptians' http://www.amazon.com/Ancient-Egyptians-Jeremy-Sisto/dp/B000244FGE/ref=sr_1_3?ie=UTF8&s=dvd&qid=1235505411&sr=1-3 that describes a case of tomb-robbing that was discovered, with a hapless tomb-robber meeting a 'sticky' end on a sharp piece of wood...
Bonnie and Clyde were notorious robbers who were gunned down in the end but that doesn't mean that nobody makes movies about them or wants to play characters like that. D&D games are known to end in total party kills, too. The most noble character in the Trojan War might be Hector and he not only dies and has his body desecrated by Achilles but Achilles' son Neoptolemus tosses Hector's son to his death. Moses leads his people out of Egypt and never gets to enter the Promise Land. There are plenty of bittersweet stories and tragedies going way back.
I guess my point here is that I think you are taking a very narrow view of how a Mesopotamian or Bronze Age game might be played when there are several ways to approach that place and period. In some ways, there's nothing wrong with playing a game in that period like episodes of Hercules and Xena or even the Scorpion King movies or Conan. No, it wouldn't be high art nor would it fit everyone's idea of the period, but I'm not sure it would be as far off as some people seem to think it would be. And even if all the players get out of it is replacing the Medieval trappings of traditional fantasy settings with the trappings of the Bronze Age, instead, that might be all they really want since I think few groups have the knowledge and skill to play characters even moderately authentic in any period of history or any country other than their own.