Simultaneous access sucks hard on NFS or AFS. The old protocols definitely don't win here.
I don't know what you mean by running applications directly from the network. We're talking about storage protocols, no? Storage is not related to applications. Dropbox is not intended for remote hosting of applications and nobody uses it for that purpose. There are different products such as EC2 for remote execution of applications; they would be the proper basis for comparison. If you mean that NFS supports things such as root filesystem over NFS, this is a comparatively easy problem to solve. For example put your filesystem image in the cloud and point your hypervisor to it (there are other ways too). Besides, the market demand for this feature is tiny compared with the market for personal storage.
Sorry for having to guess what you mean, but you really should be clearer about what you mean. To me there's no question that cloud storage solves a lot of really hard, previously unsolved problems that normal people find useful to have solved. In the end, if the old stuff does A, and the new stuff does B, and B is much more useful than A, then that's a big improvement, and one should not trivialize this accomplishment as merely "different functionality".