They can, they just choose not to. It's mainly a macho hockey thing - anyone who wore one would be considered wuss, as those players who wear even the half visors are (especially when they leave them on for fights, as Matt Cooke did when Shawn Thornton challenged him over his hit on Marc Savard last year). Players might also give the reason that the full cage obstructs vision and the full glass masks are prone to fogging up. But they are definitely allowed to wear them - sometimes after a player has broken a nose or cheekbone you see them wear a full shield when they come back. See for example Zdeno Chara: http://hockeyindependent.com/blog/wp-content/uploads/2010/07/chara.jpg
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Some NHL goaltenders do wear some form of neck protection, but it is not required equipment for 'skaters'.