I think the lack of projects also leaves out the opportunity to innovate: beyond the points that some of you have mentioned, not gluing yourself to the file system layout also give you the opportunity to do things that go beyond what you can think of when relying on the filesystem alone.
One idea, for instance, is to add not a directory to a project, but a repository. You'd have access to previous versions of the file with a right click, peruse the commit logs in the morning over a cup of coffee, etc. Since not every file needs to be tracked by git, mirroring the file system would not be sufficient.
So then TextMate would know that the repository (or repositories, e. g. your local and the »official« one that you share) belongs to your project. You could add metadata, sort things as you wish, add settings, etc.
Open the project folder. Bam. You're done. You've opened your project. If your project contains a bunch of directories lying around your system then, my friend, you are doing it wrong.
I think it's less about replicating functionality that projects offer, but that for certain jobs (and people), organizing your stuff in projects is just easier than to do it via the file system.
I also second the sentiment that using symlinks or so are not always an option. I use Dropbox to collaborate with colleagues on research projects. I keep one bibliography file. If I were to use a symlink, this would mess things up for my colleagues.
Beyond the fact that certain things cannot be replicated, it's a difference in styles. Some people merely prefer Projects to doing it on the file system level.
Max