It doesn't need to be a web application. It's just that making it a web application gets you you stuff like mobile support and synchronization between devices basically for free.

In 2019: Flip the question. Why does it need to be a desktop app and not a web app?

Web apps are nice, because most people have multiple devices nowadays. Having your data located on just one device can be rather annoying. Or having to setup a desktop app and a web server for synchronization isn't as nice either.

It also might be, that lots of people don't even know how to create desktop applications anymore, but most will have done something on the web already.

Why this is helpful to me: analyze data on desktop, input transactions on the go (on mobile) via web interface or with an app (the API).

If you have multiple people managing the money in your household (e.g. marriage), a single desktop application gets awkward in a hurry. Plus a web-based app lets you manage your finances regardless of OS (Windows, Linux, Chromebook) or device (computer, tablet, smartphone) without worrying about whether the author decided to support it or not.

Why is this being downvoted? It's a genuine question and I'm curious about it too.