I'm hesitant to respond to this because it's more complex than you write it. Some of the senior members will be able to provide better insight into how specific memory pattern usage would ultimately increase bandwidth.
Esram is designed to only hold 2/3 of the back buffer and textures are streamed into esram when it needs it, it does not need to stream the textures back. In fact it's almost useful to look at ESRAM as nearly a black hole with the exception that the render target will eventually come back.
The remaining space in ESRAM is used for scratch pad work which is a majority of where the bandwidth should be consumed.
Bandwidth is a unit of transportation. I've never considered it a measure of speed. Speed is a measure of velocity and distance, bandwidth is an aggregation of data moved over a set interval of time. As such you would agree that electricity nearly runs at the same speed as light, so why is 56K on a phone line yet we have so much more on OC48? It's because OC has multimode frequencies all sending different data in that all at the same time. The data isn't necessarily flowing faster than light, there is just more light than can be processed. In telecom we aggregated smaller data streams into larger one and those larger ones go cross country over large optical pipes or through satellite or whatever may be the case, but we are still bound by the same speed which is the speed of energy.
edit: that example might lead to OT. So lets make it simple. I have 8GB GDDR on PS4. I do the following:
int hello = 8;
int world = hello;
If I have 4 GB GDDR and do the same thing, will 8GB do that same statement in 1/2 the time?
Spoiler
So bandwidth is not speed, bandwidth is about how much data can be fit. When you do the following statement:
hello = world + hi + var2+ var3+ object12 * happyworld;
Then we're pulling lots of data from different locations all at the same time that having a wide bus can pull from. If I don't have a wide enough bus I will need to spend additional clock cycles gathering that data before I can begin processing.
The GPU is an aggregator of bandwidth, whatever lines are free for it to pull and push is what it can work with. When you made the example of 2 fax machines capable of doing 1 fax per min, vs a fax machine that can do 2 fax per minute, that is a comparison of processing speed.
You haven't sold me on why it all needs to come from a single pool or why it needs to be 8GB yet.