Wouldn't such an approach either:
1) require a lab to make a heavy investment in online infrastructure and support personnel, or
2) rely very heavily on outside service providers for access and retention of one's own data?

I would worry about putting something as valuable as my own data into the "cloud". Good article here on this, by the way:
http://ascii.textfiles.com/archives/1717

Any system that is going to see mass acceptance is going to have to give the user a great deal of control, and also provide complete and redundant levels of back-up of all content. If you've got data scattered all over a variety of services, and one goes down or out of business, does that mean having to revise all of those other services when/if the files are recovered?

I'd rather rely on an internally controlled system and not have to worry about the business model of Flickr or whether Google was going to pull the plug on a tool I regularly use. Perhaps the level to think on is that of a university, or company--could you set up a system for all labs within an institution that's controlled (and heavily backed up) by that institution? Preferably something standardized to allow interaction between institutions.

Then again, given the experiences I've had with university IT departments, this might not be such a good approach after all.