For the past ~10 years, it seems like internet speeds here in the US have stagnated. Probably 80% of places I've been to or lived have been 100Mbps-500Mbps.
I'm curious what things would look like if the internet was suddenly 1000x faster.
Would there be new apps we could build? Would it enable novel use cases?
For non-users (datacenters, companies, cluster systems etc) that might mostly help with distributed storage, but again, you'd also need all the other things, because distributing anything like that also means every piece of the puzzle needs to be able to handle it. Within a datacenter or a public cloud, even top speeds of 400Gb/s (which is less than half of the thought experiment) is at such a high tier that it isn't useful for individual applications or nodes.
Something that would actually make an impact after you get to around 2Gbps would be lower latency, lower jitter, net neutrality (including getting a full connection with no administrative limits), and more peered routes. More bandwidth doesn't really do much, especially if you can't use that bandwidth anyway if the amount of connections, the latency and the computing equipment doesn't scale with it.
When you have low enough latency combined with high enough bandwidth you can start to actually get new apps and also develop novel use cases (imagine a CPU-to-CPU interconnect that can span continents). But the speed of light (or some more exact latency-per-distance quantity) prevents that.
Beyond the likes of BitTorrent and Gnutella we're not likely to see network-based ideas that are currently impossible due to limits on the average speed. Perhaps the real problem right now is the lack of universal availability of reasonable connectivity.