Flat design is a relatively new trend (at least in popularity) and as such it's not going to be as widespread. for the most part, updating a website's visual usually consists of simply changing the CSS Stylesheet whereas when working with a desktop application, changing the interface and colors is a little bit more involved. Plus, you then need to push an update to your users and all in all it's just more of a cumbersome process than doing it on the web. I'd also argue that desktop applications are ever so slowly becoming less relevant -- most new products are now being developed on the web.
Though that doesn't mean we don't see flat design applications. of course, anything by Microsoft is being converted over to this flat design (i.e Office), they even took it as far as flattening their own logo. The Adobe sweet while maybe no completely flat, has certainly taken steps in the past few versions to be more flat.
Flat design is also mobile friendly, if you're working with buttons and they are flat they can be easier to read on a small screen as opposed to some crazy gradients.
Of course these are just my opinions and there's probably someone more qualified than I to speak on this.