This study quantifies the gains from a fairly macro perspective: https://www.ericsson.com/news/1550083. 0.3% GDP growth for doubling internet speeds seems reasonable and is not unsubstantial. My guess is doubling internet speeds is cheaper than e.g. adding public transportation to even a small number of cities.
There are also huge network effects which may cloud the benefits, until suddenly some mass market consumer application makes it blatantly obvious. Youtube and Skype are so successful because a significant portion of the world has access to fast Internet and microphones/cameras to the point where I can talk to my grandparents in rural Russia despite not being able to visit them in person for almost a decade. What if our Internet was fast enough and our displays cheap enough that working remotely or across international offices becomes as simple as installing several wall sized monitors in geographically spread out rooms? The display tech will get there eventually (just look at the stuff Corning is working on), but if there isn't any infrastructure to utilize the tech it will take much longer for mass adoption. It's a chicken and egg loop but while the technology improves, we have to make the positive decision to invest in infrastructure even if the benefits aren't immediately clear.
I think the lack of content today isn't due to a lack of purpose, it's a lack of demand because the technology isn't quite there. In the next few years way more people will have 4k TVs and internet connections that can handle streaming 4k video. I already see a lot of people upgrading to bigger TVs as prices fall, where 4K will really matter.
It makes sense. The better and more extensive the networks that make up the economy, the easier it is to meet, transact, collaborate, move physical and digital goods back and forth, teach and learn from others, expand markets, compete, etc.
As people and things become more connected physically and digitally, the networks that make up the economy get larger -- by definition.
In my mind, this is a question of productivity as well not just about downloading movies or watching 4K. If everything is cloud based, we need the cloud to be faster as well as any interaction between the cloud and us to be as fast as possible.
I understand the idea is, if we build massive pipes, life changing uses of the internet will be invented that cannot even be conceived in today's bandwidth-strangled world.
If we had better infrastructure, we would take advantage of it, I guarantee you.