I never really noticed the graph thing before, but now that you mention it I do kind of miss that. Even if they weren't very accurate, being able to get a vague sense of how everyone is doing was kind of nice.
The city number and toughness thing is really, really easy to explain, though: They want to prevent snowballing. In games that don't do something like this or don't do something like this very hard, you want more cities which allow you to get more cities which in turn gives you more cities. Once somebody's on a roll, it's hard to stop them because they have more everything, including the tools to get even more of everything. Once somebody's taken a setback, it's hard to get them back into the game because they have less of everything, including the tools to get more of everything. And if the cities can't defend themselves, then it's really, really easy for either situation to happen because one side or the other just rolls a superstack up, takes a city, and then does that a few more times before their opponent can properly react.
This showed up well before Civ5, by the way. As far as I've noticed, each Civ game has been a little less spamhappy and conquest-friendly than the one before it. Civ5 just went a lot further than previously, realized that "you pay more money" was not a terribly good deterrent for owning the entire world, and came up with a bunch of little related systems (vassal/puppets, city states) to support the new intended paradigm.
As an aside, BE Health is a bit different from Civ5 Happiness. Health is harder to get than Happiness was, but the penalties for having it are milder. So in Civ5, the general idea was to never be Unhappy and fix the situation if you were. In BE... ideally you want to be Healthy, but you're not missing out on that much if you're a little in the red for long periods of time. The very first tier of effects is slightly slowed population growth, for instance, which while bad is a bit of a self-correcting problem.