Probably not online banking, but a lot of game applications or media intense applications in the browser are going to get real squirrely if they cannot detect the user's configuration.
Even things like the GPU make and model can end up necessary because the webgl mechanisms for determining those things are allowed to lie (i.e. I've seen cards that report in the gestalt data that they allow various features, when those features are in reality implemented in software and therefore basically unusable).
