This can be enabled in truth by names as well. Most notably obviously for race/national origin. A notable study found that the exact resume received fewer call backs when the name was a typical white name vs a name indicative of ethnicity. To a lesser extent you can also consider age in relation to name as some names have drastically increased or decreased in popularity over time.
This makes me think that a productive solution would have to take place in HR as opposed to grass roots. Ideally you really want people to review candidates initially without benefit of name or face and only after selecting a subset view potentially biasing information.
Maybe there should be a HR mode for LinkedIn which by default hides these details and shows other items while allowing you to make a saved list of prospective hires to pass down the food chain.
But it's also a great way to enable racial and age discrimination: see the face and decide you interpret all the rest of the context in the profile differently (even inadvertently).
Sure, you'll know the race / age / etc eventually, but at least if the person is in the door they have a chance instead of getting chucked in the bin during screening.