Sure, you can compile them on any desktop platform. But what about mobile platforms? Sadly our usual understanding of "cross platform" seems outdated when faced by mobile platforms, where end-user apps cannot be compiled from C without hacks.
Granted, a desktop interface will be inconvenient on a mobile device anyway. But it would be great for a software if at least most of the backend logic shared its code across ALL platforms, including mobile, for consistency. The Mono implementation of Microsoft's CLR specification could be used for that, but I don't think it is too popular right now.
For a start, the browser-based desktop applications would provide a cross-platform software repository for convenience.
You mean like they did with Google Reader? No, no confidence there anymore. But if they succeed in pushing their app-store, it will become unlikely at least.
The only truely slow Windows I've known was Vista. Granted though, Windows notebooks tend to suffer from bloatware, slow hard drives and lackluster long-term driver support. Same problem as non-Nexus Android basically, except that Microsoft ships at least security updates and service packs in a centralized fashion.
Mac OS' better reputation comes probably mostly from the "hardware and software from the same company" approach that prevents such exploits at the cost of higher prices and the absence of niche solutions such as dedicated gaming notebooks or convertibles.
More importantly though, most people will hardly leave behind all their usual desktop software at once to switch to Chrome OS. They may however find Chrome Apps useful and gradually use more and more Chrome Apps and ultimately may reduce their Windows box to a fall-back solution in case they need PowerPoint.