For me, often, it's just a bandwidth issue. If a colleague has a 12 GB movie they'd like to transmute, a local app might be a possibility, but an hour long upload followed by a 20 minute long download won't be.
The creator mentions in another post that the service does indeed upload the data to a server for processing. But, in general, it being a web app doesn't mean it uploads your data any more than a locally run application might. A web app can just as well do the processing in the browser without it ever leaving your machine.
On what are you basing these expectations? Uploading means transmitting data to a third party. One could write a CLI that does just that. One could also write a web app where the processing takes place in the browser and the data never leaves the machine.
The difference is the web app runs within the browser sandbox while the CLI executes with user permissions.