I think there are a lot of benefits to a web app here including:

  - Cross-platform support
  - Collaboration and sharing, especially with unregistered users
  - Speed to get off the ground as a new user
  - Automatic updates for fixes + features
  - Integrated live support
  - Great open-source community

The largest downside for me is less robust offline support, but that's improving. I'd be curious what the most important missing pieces are for you. Would love to minimize those downsides!

Is your question rhetorical? In case it's not:

1) Web applications make it easy to require monthly subscriptions, which many people don't like but is great for companies

2) Web applications can be more easily monetized through ads

3) Web applications can be updated for everyone more easily than a bunch of native installs, potentially reducing support costs

4) Web apps are a solution (not the only solution, but probably the easiest solution) to cross-platform development

I think the native platform is well covered already. Musescore and Tux Guitar (which despite the name is available cross-platform, not just on Linux) do pretty much everything you might possibly need as far as simple songwriting goes, plus a lot more.