Could well not happen, but the most likely driver of slimmed down websites, anyway, would be a desire to make them load better in India, Africa, parts of Latin America and eastern Asia that have low connection speeds. Not saying that's how it will go, but it's feasible that to get to the second and third billion internet users, you need to be slimmer.
It's still kind of a niche, though. People who don't live where decent internet access is readily available also tend to not have enough disposable wealth to make great business targets, especially for social media and other sites that sell eyeballs rather than widgets.
On the other hand, one of the first things people with disposable income want today is good internet access, so as income grows for the middle five billion (and it's growing rapidly), there's tremendous market pressure to supply them with faster internet - maybe not up to the standards of the top billion, but not "low tech" either.
