Web app? No thanks.
You assume we have a network connection. Never assume: it makes an ass out of you. Some tasks can be presumed to have a connection, email & web surfing primarily, but others like a spreadsheet, document editing, calculator, solitare, or just looking at family vacation pics are not among them. Sure we MIGHT do those things through a web interface, but what's the point?
I've got work to do, I need it to work just as fast as the desktop running the program, not to have to wait for a site to load, refresh between each action, & eventually cough up the results. If I'm editing video & have to wait for a web based interface to react to the task at hand, it's going to take FAR too long to be of any real benefit to the user. If I'm dealing with a locally stored, locally generated, & locally maintained database file, relying on a web interface to interact with it seems rather counterproductive.
A SmartPhone may need a web based application in order to Get Shit Done, but then I can't imagine writing a PhD dissertation on your SmartPhone...