Which network and which latency? My local network runs audio way below the Haas limit - I can record over the network without incurring any latency penalty.
Comparing local-network performance with "random" cross-internet traffic IMHO isn't very useful, because there is a wide range for internet latency.
My wired desktop gets DNS responses from 8.8.8.8 nearly as if it were in my network, in way under 10 ms, ping responses in 2 ms or so. Accessing websites hosted in e.g. Korea takes >100 ms.
Add a congested wireless connection somewhere (WLAN or mobile network) and you can add another few hundred ms. And neither cross-continent nor congested wireless latency is going to go away.
Perhaps I should have been more explicit - comparing local audio traffic to local web traffic, there's a heck of a lot of difference. That would be the stacks.
I said audio. I provided this as a counterexample to the stated thesis of your post. There exist things that can be done over a network such that latency is not an issue. I am obviously not pulling data over a cross-continental link.
FWIW, the protocols I write at work can do a full data pull - a couple thousand elements and growing - in under a half second end to end. I don't know of any HTML/Web based protocols that can even get close to that over localhost.
So yeah - we know the Web is an utter pig. My point is that it probably doesn't have to be.