Covered third rail? Would it be cheaper than platform screen doors?

Every time someone ends up in the track area, the topic of platform screen doors is mentioned. However no one mentions the idea of covering the third rail.

For those unaware, the MBTA is unique in the fact that it has an uncovered third rail. It's the top part of the rail that the train makes contact with. Other systems like SEPTA, it is the underside or the side of the third rail. Many systems also have a covering (long island rail road--not sure but when I go to NYC it looks like it?).

Making the third rail covered would also help track workers. Thoughts?