The Circle Of The Black Thorn thing on Angel seems rushed because it was. They didn't find out from the network that they were getting cancelled until they were two-thirds of the way through the season. They had mere weeks to tie up four and a half years worth of show. Given those circumstances, I'd say the results are pretty impressive.
First of all, Joss Whedon himself is at least somewhat to blame for getting the show canceled because he was the one that insisted that the WB give him an early answer. Had he not been so insistent and waited until the end of the year, they might have decided to take a chance on renewing the show since its Season 5 ratings were an improvement over Season 4.
It's also possible that the show would have been canceled anyway. David Boreanaz & 20th Century Fox both wanted more money and it was never a cheap show to begin with. They might have priced themselves out of the market anyway. We'll never really know.
But considering Joss Whedon insisted on an early decision specifically so that they could plan ahead for the series finale, I'm surprised that it feels quite as rushed as it did. Even if they didn't know for sure whether the show was going to continue, they had to know from the outset that cancellation was a strong possibility. The show had already been on the bubble for much of Season 4. And I remember feeling pretty sure from the outset that Season 5 would be the last season. And even if it wasn't, they still would have needed to do some kind of big finish for the season finale. I don't think they needed to do much but I think at least a little extra early prep work to sow the seeds of the Circle of the Black Thorn would have been appreciated, even if it was just showing the symbol in the background a few times.
Season 6 of BtVS was just unhinged. I don't know why, I don't know if maybe something went wrong behind the scenes?

But for whatever reason, all of the ducks lined up at once... and created an entire season that was just totally over the edge.
I don't know that anything behind the scenes "went wrong" per se. I just have a sneaking suspicion that, left to their own devices, Joss Whedon, Marti Noxon, & Jane Espenson can be their own worst enemies. They all struggle so much with the notion of ever letting their characters be happy. I think Season 6 was just a perfect storm of all of the characters being miserable all at once. Whereas before, the show was better at alternating and having some characters happy while other characters were miserable.
I also wonder how much we might have to thank WB network interference for keeping those more morose tendencies in check during the first 5 seasons. I don't know how it was for the
Buffy writers, but I know that the writers on
Roswell remaked that they had much more of a free reign on UPN than they did on the WB. (On
Roswell, part of that manifested in the fact that everyone seemed to have much more robust sex lives in Season 3 than they did in Seasons 1 & 2.)
I thought Buffy was a far better show than any of the other Whedon projects, especially in hindsight, largely because its central conceit was the most interesting. Essentially Buffy's life represents a failure to really grow from a relatively average young teenager into a well-rounded normal human being.
You've got a point there. In that respect, the show was very well done. But it's a real bummer. Who wants to watch a show about that?