I think I should voice myself a little, I absolutely adore BB, may be because it was my first Souls game. Last February I started to look forward to play Dark Souls 1, and now I'm finishing the second DLC of Dark Souls 2 (I already finished the main game)
I think I will kind of address how I think about the same points you touch, I'm in a much cleaner mind than people in the tantrum of the release of DkS2 and the much hate it was thrown:
1) I don't think the "connecting world" aspect became so important as the area "connecting aspect" because as I interpreted DkS1, one of the things it made me personally awe was how the many areas inside it, except for some few like Tomb of the Giants or The Duke's Archives, have more than one way to initially enter, potentially altering the timeline in which they can be played, some can even be skipped altogether, like The Depths. This part added not only a replay value to DkS1, but also a variety in the gameplay it had on the origin. In this aspect I totally get that DkS2 is an inferior game to the other Souls.
Now, I haven't played DkS3 yet, but in BB, there is somewhat of a difference, the areas are not as connected as DkS1, in fact they follow more DkS2, but the areas themselves are bigger, and more intricate, they follow a maze like structure that connected several parts to a single area, with a lamp.
what I've come to realize after loving the DLC of DkS2 much more than the main game, is that the areas encourage a lot more of exploring, they aren't a corridor in a single direction, they act again like in DkS1 main game, like a big maze, but instead of many areas acting like a maze, the areas themselves are mazes, similar to BB. I believe From Software evolved the idea of the DkS2 DLC into what BB became.
2) The Fast Travel design didn't compromised much more than what the "checkpoint" placement did. BB for example follows more the line of DkS1, veeeery few lamps, but they make them enough to connect to all the little parts of an area, an example: Central Yharnam has only 1 lamp, but is so well positioned and the area is so well designed that only this lamp is needed, you can only warp here, but it never became an ordeal to get to another part in Central Yharnam, and also while BB has the same warping mechanic, some exploration is still required to get to where you need to go.
DkS2 in this regard is a lot weaker, and I only need to say this: "why an area needs to have 5 bonfires?" This is one of the questions I got when I was playing the game. I believe this has to do with how linear it was. I don't think the problem was the leveling in another area or how it breaks the immersion, it has to do with how much you have to give up by leaving the area by traveling back to where you want.
3) This is the point where I don't agree with, The builds in DkS2 further expands the builds made in DkS1, and whether the ATN did a lot of damage to magic/miracle builds in DkS2, the variety of the tools and the little touches (like casting time) made it better than what DkS1 accomplished. It is just a matter of finding a correct tool.
I found myself using far more weapons and tactics for my DkS2 run than what I ever used in my 2 DkS1 runs
4) The design... something here went wrong, you nailed what I felt, they never feel unique and rather look... bland.
5) The bosses weren't weird and that's what I think it hurt... Much of the Soul series revolves around the unexpected discoveries and how the player is surprised with bosses and their weird mechanics and turns. You won't surprise anyone with a Dragon Rider... well... what about TWO Dragon Riders? ...mmm.. nah
Another thing I believe hurt a lo DkS2, there is a constant inconsistency in the Lore, what is Nashandra? what does she really want? why is she proving us...
What are the Giants? anyone's guess because the game never really clarified this.
Even the opening cutscene shows a lot of things that we won't really know what is, remember DkS1 opening? That thing couldn't be more clear, it lays the path of the player to understand what is the state of this game.
DkS2 is a good game, I like it, but it is, of course, a let down from other Souls games, and I completely love DkS1 since I played it some months ago. I even love the DkS2 DLC.. but while I like DkS2, I don't love it...