Having written a (still running) patient flow management system in html3 + hidden frame + javascript - sadly no ajax it is my belief that with proper care a web interface can be used in place of certain local apps. For processes that do not involve complex graphical/video wizardry (i.e. most business apps??) HTML[5] seems adequate enough. This includes many day to day internal business applications where the benefits of management, maintenance & security outweigh most of the drawbacks: bandwidth, hw compatibility, less seamless UI etc.
Separating out the business data and logic/api from the interface also does wonders (ye olde "n-tier" architecture) for the client-side concerns. Everything properly validated through the server-side logic layer.
Migrating an existing local app to the web can be a headache though - then you run into potential usability issues with user expectations and proper program "flow".