My reply comes quite late, but here's my summary for the thing I was waiting for for quite some time:
So this finally happened.
My personal opinion is that we just got rid of the worst companion in the way it should've happened which is also the worst way and that's ok.
It is the worst way to get rid of the companion, because the whole death scene was overlong with the setup, the wait, the goodbyes and that slow-mo mute raven scene. All of this to make the character we never cared about die. All of this overshadowed by a cliffhanger for a two-part episode. And I don't think I cared about Clara. Ever. Whatever her interactions with the Doctor were, ever since her gimmick "mystery girl" setup was done and she became a normal companion, we got the flattest, most unrelatable character on the show with a clear Mary Sue problem.
The first problem is that Clara had no personality. Even taking the basic personality test (Watch Plinkett's Phantom Menace review for an easy introduction), there's nothing to say about her. Is she sweet and curious as Rose? Is she funny like Donna? Is she quirky like Amy? Is she headstrong and willful as Martha? Am I seriously using Martha as a good example here? Damn, even that girl had something I could talk about!
Whether Colemans' performance had issues or whether writers' inability to structure the character manifested here, her personality ended up being flat and changed depending on whatever the story needed her to do. That's the worst kind of character possible. She's always funny, always too good, always barely emotional. It really doesn't help that the character has very little framing: her non-Doctor life is utterly boring and devoid of interesting characters, and the only big arc with Danny Pink is once again unrelatable and boring. Two flat characters, dating 101 scenarios, no in-depth relationship doesn't make for good TV.
So in the end Clara says she's become reckless after Pinks' death. What kind of bollocks is that? Wasn't she reckless ALL the time? It's just writers putting in words to trick us in believing there's an arc while there isn't one. It's like her actions when Danny died, her emotional swings, they are all in words and in the end her real character never changes, which leaves us with a statue instead of real human being. Her characters' words don't coincide with her actions and her changes are constantly retconned or reset.
Another consistent problem is that Clara doesn't react like a normal person would to things happening around her. This is crucial in a companion who is supposed to give us a relatable view on these stories in which the Doctor is alien and doesn't do things like a human would, with flaws and all. Every companion before had at least a basic arc of wonder-confusion-acceptance-transcendence, which is basically adapting to new worlds not unlike going to live in a new country only 100x times worse. With Clara she's in on day one, always feisty, never in awe, never in wonder. Clara having barely a non-scripted, not one-time, real character flaw or trait denied me relating with her and thus made all these stories seem distant with two superhumans dealing with alien stuff.
Last thing is that Claras' death in the end is really pointless and has no impact apart from the verbal one we saw in this episode. What happens if she dies really? Her interaction with the Doctor is emotionless, like a tacked-on contractual friendship. All their on-screen stories show little emotional connections, the writers have to start an episode by showing how much fun they have together on the adventure we don't get to see. To add to that she lives alone, barely any friends or normal people in her life. I'd say nobody on Earth will miss her in the end. Therefore there's really not much investment in her death.
The good thing that came out of this episode was the fact that we finally got unshackled from her. I don't hate Clara, but she was holding the Doctor in this emotionless procedural state for too long. It's time to bring some humanity and heart back to the show and a new proper companion is essential for doing so.
PS. And that's why Ashildir, Osgood or anyone else who's already "in" on the Doctor would make terrible companions. We need a relatable person not superhumans.