Because of Privacy concerns! The thinking is that few people would enter their email and email password on a 3rd-party website, having it as a downloadable software ensures the privacy of users
The biggest difference is that it's way easier to see where you're data is being sent in a browser, since it has built in tools. It's very hard to monitor native app traffic that is sent over SSL.
You, Your mail (provider) server.
Vs
You, the server hosting the web app, your mail (provider) server.
Unless you run uMatrix or uBlock Origin (same code in both as far as this feature is concerned), of course.