One argument against requiring the hyphen in such situations ("first-quarter touchdown", "emergency-room visit") is that doing so encourages constructions that

One argument against requiring the hyphen in such situations ("first-quarter touchdown", "emergency-room visit") is that doing so encourages constructions that are ambiguous if spoken aloud. Since the hyphen never makes it into speech, you end up relying too much on the punctuation to convey meaning. Note that certain punctuation is often spoken aloud for instance people often say "quote" (and maybe "unquote"). Other punctuation such as exclamation point and comma can affect how it is spoken. Technically you can speak very slowly and group words together and use a bit of accenting to indicate how words are grouped, but still. I generally don't use a hyphen unless it is absolutely needed to make it clear. I find them kind of ugly and can break the flow.