It's not about latency, but about overall performance. Rendering on the server is slower than rendering on the client, because the server may have to deal with a thousand requests per minute whereas the client doesn't. So you push the logic to the client and let the browser deal with it until talking to the server is actually necessary (e.g. when the time comes to submit the data). Therefore client-side frameworks become a kind of distributed processing of application logic.
Furthermore, you shouldn't take latency for granted. Many users are on choppy mobile connections. Waiting for the server after every action results in a really bad user experience in those scenarios.
I'm not really buying it... Rendering on the server seems like a solved problem to me. Web apps scale.
Sure, you can save servers by offloading work on the client. But I think your server cost is absolutely dwarfed by developer salaries. I guess it depends on whether you have more front end people or back end people. Good front end people seem to be just as expensive and rare as good backend/C++/Unix/distributed systems people these days.
On mobile, most web apps are a disaster. They are certainly a lot worse than light HTML. Never mind waiting for the server on every action -- try getting the app to load in the first place! The Android and Chrome team have numbers on the astronomical rate of user-aborted or otherwise failed page loads on mobile. On mobile, users see the white screen for 5-10 seconds (probably waiting for your 10-50 round trips for your JS, CSS, heavy image assets, and especially third party JS) and then give up.
I hand tuned web apps (vanilla JS5, no libs/frameworks) and opimized them for mobile, and they are very fast.
But most don't care and use bloated JS libraries/frameworks and the end user has to wait several seconds until the 1MB JS file loads over a cell connection or even crash the mobile browser because the site owner thought it is okay to integrate 30 advertisement and analytics third party JS files.
Furthermore, you shouldn't take latency for granted. Many users are on choppy mobile connections. Waiting for the server after every action results in a really bad user experience in those scenarios.