High-bandwidth signals require more power to travel a given distance, low-bandwidth signals go farther on less power but transmit less information. Intuitively this is why you can go worldwide with CW (Morse code) on just a few watts of power, while a SSB signal on the same frequency doesn't go far at all. But I think you can mathematically support this by playing with the bandwidth+power terms of the Shannon-Hartley theorem.
If we want to transmit a given amount of data per time unit, there are two natural extremes. We can either transmit it at the average data rate necessary, or we can race-to-sleep by blasting it out as fast as possible. I'm not sure which is more efficient given that SNR is inside the log2 of the S-H theorem, it depends on the relationship between SNR and bandwidth as you spread a given quantity of RF power thinner and thinner. Based on the log2 I would think this is an inverse-square kind of thing, making it an equivalent tradeoff.
Showerthoughts: because of the Inverse Square Law, it's probably more efficient to make a mesh of multiple small hops than a single long shot. As the spacing of the mesh decreases to zero, you end up with a wire.
Also, check out the ESP8266 chip, it doesn't have a BTLE onboard but it does handle the "SOC with low-power wifi" thing.
I know all about it. Still won't run on a coin cell.
Nobody will build a 2mW WiFi chip until Apple forces somebody to build it. Then EVERYBODY will rush to build it. Then EVERYBODY-1 will go bankrupt when Apple doesn't use their chip.
It's the Zen of Hardware.
Not as much as you would think.
Battery life in the embedded space is mostly defined by how much you can stay off and what your leakages are rather than what your active current is--since you can quite often just stay asleep a little longer.
Most of these microcontrollers are in the same range for leakage and are at the point where you have to start considering other leakage sources on the board (capacitors for example).
It's Amdahl's Law in action: the big contributors have all been smacked down pretty much as far as they can (sure, you might get 10% here or there ... but it's going to be real work now) so now getting overall performance isn't so easy.
If someone really wanted to get my attention with their microcontroller, they should produce a combined BLE/WiFi chip where the WiFi can be run off of a coin cell battery like BLE (that would mean something like 2mW transmit power rather than 200mW).