The benefit of installable client software is that the encryption software and the relaying party (your e-mail provider) are completely unrelated and separate.

The benefit of installable client software is that the encryption software and the relaying party (your e-mail provider) are completely unrelated and separate. So if I use GMail and encrypt my messages to Bob with GnuPG, than no matter what GMail does with the encrypted message, it either gets delivered securely (and is verifiable by Bob as having been written by me) or not. Any adversary would have to compromise the source of my operating system's GnuPG version (or Bob's), and have access to the messages themselves. The browser model explicitly trusts the remote server to provide whatever JavaScript code it sees fit, so if your e2e webmail provider is compromised, you get a backdoored crypto library that works as far as your browser and you can tell. It all comes down to trust of course, but the separation of concerns adds a very real layer of security, and I trust Debian and its maintainers (and the experts who scrutinize these things) more than a single commercial e-mail provider.