Storyline reasons. With the decline of the Empire, it just kind of...broke apart, and the Synod and College rose in its place. I imagine (hope) something similar happened to the Fighters Guild, being officially chartered as well.
No reason, however, why criminal organizations like the Dark Brotherhood and the assorted Thieves Guilds would die, however, although I hope that they work a little differently than in the past. And that the former has perhaps a more...creative name.
True, but I would think that organizations like the Brotherhood and the Thieves Guild would depend more on the personalities of the leaders who keep them together and keep discipline. As for the name, it seems that it's usually the name the peasants commonly call them. The people didn't like the name Syffim, so they called it the Fighter's Guild. Thieves guild is an informal title because nobody would name such an organization unless it was personality driven, like the Corelone family or something like that.
Mages guild is gone? Is it to diversify magic styles, or is there a storyline reason?
It was part of the Infernal City book, in a passing mention. We don't know anything about the two factions that were supposed to have replaced it, or if they would have been widespread, or if they have lasted over a hundred years to the time of Skyrim.