Well for the theives guild, why wouldn't they want you if your the head of the mages or Fighter's guild? That's penetration of a potential target's command structure at the highest level. They could do incredible amounts of robbing without worry. And for the reverse, how would the fighter's guild or mage's guild know your a member of the Theives guild?
As for the Dark Brotherhood, why would membership in a secretive assassin's cult keep you out of the Mage's or Fighter's guild? These guys don't exactly give out their membership rolls. How would they know you are Dark Brother? Are the dark whispers of Mephala compromising your identity to them?
The only ones you possibly have an arguement for is mages/fighters guild exclusion, but, get this, there is no mage's guild as of skyrim. We also don't know what the policies of the College of Whispers and the Synod are. So any arguments about them are bound to be flawed.
as i posted later on the only guild that could be uber secret is the DB, even that is tenious. the first time you go into a chapel and the nine divine wont bless you from the altars will instantly let everyone know that your are not a very nice person. thats going to raise questions and eventually a bunch of mages will find out about why their dear leader isnt being blessed.
even if your a member of the thieves guild, you are going to be known. local constables would know that you hang out with known members of the guild. the only secret parts of the thieves guild are the vendors and the head honchos. in oblivion, Pontius Assius or whatever his hame was got one of the thieves guild women to turn on the guild so obviously the local law enforcement knows about who is who. people are going to know if your hanging around the seedy part of town and walking around rich peopls houses at night. the problem the soldiers had was actually catching people in the act.
they might not have a problem with you being a low level member of the mages guild for the reason you stated but they are going to have an issue when you get to the higher ups cause of conflict of interest. its like having the same guy in charge of the DNC and the RNC. would anyone from either side trust that guy to run their campaigns?
the mages guild would NEVER accept someone in who was even a low level member of the thieves guild. they might give you a mission to infiltrate and find out something but after that you are expected to drop them like a rock.
the split in the mages guild will make it even more pronounced. there is a reason for that split and they wont tolerate someone from the other side trying to get in their organization.
that being said i still would love to see a double agent questline of some sort and i dont mind if the guilds allow you to be "foot soldiers" for them especially since your useful for killing dragons (who would turn that down?) but as far as getting to high ranks. no way it doesnt make sense for competing guilds.
as for the combat styles...........its not about the battlemages and combat styles. follow the money. the guilds compete for contracts and for the favor of the local lords and of course for prestige.