Has anyone ever felt that in Skyrim your rise to Arch Mage of the College feels very hollow and unrealistic? You appear on the doorsteps as an apprentice, and only once during the questline Savos Aren acknowledges that you're doing well and gives you a circlet, but otherwise there is no real feeling of progression within the College ranks. You happen to stumble across the Eye, and even when you tell Savos the Staff needs to be found, he says "someone has to do it", coming across as dismissing the thing as just a small, unimportant thing left for you to do. Then when all hell breaks loose and when you save the College, all of a sudden you become the Arch Mage...
There are several things I feel just don't make sense. Firstly, despite you saving the College, you're still very much new to the place and haven't been there for long at all. Secondly, all of the members in the College are experts or masters at one form of magic or another, implying they have great experience in magic. Finally, given the age of Tolfdir and his experience, it makes perfect sense for everyone to install him as the new Arch Mage. It doesn't make much sense at all to suddenly install the PC as the new Arch Mage ahead of all the experienced members in the College, especially when the questline doesn't have any magic requirements so you could be the new Arch Mage yet probably can't even cast any Adept level spells. The Arch Mage should be powerful and wise so he/she can actually dictate and operate the College, saving the College doesn't really justify that.
In terms of other guilds in Skyrim, the Dark Brotherhood circumvents this issue because the Night Mother actually installs the character as the Listener. The Night Mother being some form of being of supremacy of the guild even if others may not agree with it it makes sense and can't be helped (Astrid found this out the hard way). For the Thieves Guild you don't really become the leader in a way because you can accept jobs and such from other members, making it feel like you don't really have absolute supreme power within the guild, and finally the Companions there aren't real leaders anyway. You're part of the Circle but you're not really the leader of the Companions.
I think the Mage's Guild from Oblivion did this better, because as you did quests for the guild you were promoted ranks within the guild. At the very least it felt like there's a certain acknowledgement that you're moving away from just being an apprentice. In Skyrim it feels like you went from apprentice to arch mage instantly.
I feel like the game could've easily implemented something to remove this feeling, such as initially making Tolfdir the caretaker Arch Mage, but then after a certain amount of time he feels that he's getting old and the College needs new leadership, and everyone voted you as the new Arch Mage. In the current questline I don't even feel comfortable becoming the new Master Wizard at the end, let alone becoming the new Arch Mage.