"They looked at each other block."
"They looked at each other."
"They looked at eachother."
To my eye, the first and third make syntactic sense, while the second looks like a sentence fragment.
So why isn't it acceptable as a single word? By all the logic I can see, it functions as one already. I realize this is more of a rant than a question, but I would welcome some grammarian feedback on this issue if there's any to give.