You mean like repl.it or skulpt or ... actually there's a few different option with different features, but doing python in the browser has been a thing for many years.
If you have a traditional server-rendered web application and you want to add a little bit of scripting on the client side, it can be nice to be able to share pieces of domain-specific code (for example, you might want the client and server to have the same notion of what a well-formed stock code looks like).
In more sophisticated systems, people sometimes like the client to "optimistically" do the same processing as it expects the server to do, so it can update its display more quickly.
Or if you have a mostly client-side application which builds up some fancy widget tree, sometimes people like to have the server do the same rendering as the client would so that it's there on initial page load, or so that search engines can see it.
You often have the same data types on the server and the client for data exchange. When both sides use the same language, you only write these types once and it’s impossible for the client and server implementations to differ.
Saving in developer salaries is the only tangible one. You could argue there is less context switching for developers between languages, but I’ve never actually heard that from someone who builds the apps.
(There are advantages to running the same language on the server and client, and there's plenty of server-side web application Python code out there.)