On the surface this is true, but in actuality it's not. If you can consume data faster, you will consume more data given the same amount of time.
Let's say you are on the train to work and you want to watch videos during the entire trip (because it's long and staring out the window is boring compared to watching videos).
On 3G, the video will play for 10 seconds and then pause for 5 seconds to buffer. The total length of the video is 5 minutes. For the length of the video, it paused 30 times to buffer for 5 seconds each (150 seconds total or 2.5 minutes). So it took 7.5 minutes to watch a 5-minute video (a time penalty factor of 1.5).
Let's say that you're able to get a constant LTE connection. The same 5 minute video plays without stopping to buffer. So it takes 5 minutes to watch a 5-minute video. By the end of this video, you are onto your next one, while in the 3G scenario, you're still waiting for data to come through.
The 5-minute video is the same size regardless of how fast your connection is, but with LTE, it was consumed in a shorter amount of time, freeing up that "extra" time for you to consume more data whereas in the past, you would have spent that time waiting instead.
Let's assume that in the course of your entire trip on the train, you would use 50MB on 3G. On LTE, you would have consumed 75MB (50MB x 1.5) with the same amount of time. Instead of spending 1.5x the amount of time waiting, you spent it consuming data. I'm well aware that while buffering, you'll still consuming data. This time delay is average out through the whole trip.
Does behavior factor in? Sure. Most people say that people's habits won't change if they're on LTE. That's a valid assertion. But consider this. What portion of those habits were due to a constraint over which the individual had no control (connection speed)? Now take away that constraint. Are you saying that then those behaviors will now remain the same?
This is in response to your assertion that,
"Speed has zero to do with usage." It may not be orders of magnitude (100 times faster does not equate to 100 times more data consumption), but it most definitely is not zero.