But you can run a terminal in the browser. It’s a pretty common way to interact with cloud servers. And as long as the server isn’t on the other side of the planet it’s not noticeably slower than a local terminal.
The problem isn’t the technology, its the sad state of UI engineering.
I'm sure you can emulate the same performance in a modern webbrowser, it's just that no one cares, because no system administrator relies solely on web interfaces to get work done.
Increasingly, they do. And prefer to, because if it's in a browser, it's probably someone else's cloud system that they don't have to administer.
Our staff can run our ERP on a browser on a phone at the airport. I imagine it's hard to get 5250 on an iPhone. =D