I hadn't thought of just doing this. It turns out that it works in the StaticServer case because it always serves up the latest version of the file from Brackets (even if it hasn't ben saved), but it wouldn't work for other server cases (like UserServer), which don't have the same logic.

I actually think this is ultimately the right approach, but if we're going to do this, we should change the way stuff works on the server side so that all servers do the same proxying by default. See https://github.com/adobe/brackets/issues/7755 and the comment in https://github.com/adobe/brackets/issues/7606#issuecomment-42066564 for more detail. 

Another option would be to do something more like what we were doing with CDT, which would be to have it actually replace the link tag with either a reference to some temp file that contains the new stylesheet content, or actually replace it with an inline style block. But that seems messy.

The other thing to note is that this approach won't work for editing inline style blocks that are directly in HTML files, but that wasn't working in the old approach either.