I would pay without hesitation. I thoroughly enjoy the insights and opinions of many members, and estimate the fee to be some of my best-spent money in terms of "what do I get from it."
I can see 3 drawbacks:
As Zaftig stated, new people would be expected to pay without knowing what they are spending their money for. However, many pay the COS membership fee without any other insight than the available literature and website, because they consider it worth it. These sources are still available for someone considering joining LttD. I am not talking about people who might want their red card to get access to the LttD basement, first because LttD and the CoS are different entities, second, because even those who do so don't know what they'll find "down there." These persons apparently find motivation enough from the available resources. Many members who make the most worthwhile contributions here also have their own blog or website, which would also still be available. In addition, a couple of forums would still be available to the public,which would provide some more specific insight.
Another problem might be the shit-disturbers: Certainly having to pay a fee would filter out most of them, but one would still find some particularly persistent chunks, who would be doubly annoying because they would now feel entitled to our undivided attention: they paid, so they are kings. Kicking them out would breed a lot more resentment than it does now, probably with subsequent harassment.
Third point: posters are supposed to "pay their way" here by contributing in a constructive manner, but there might be a few users who will clutter the forums with unconstructive, pointless and stupid "social chat," and feel entitled to do so because they "already paid their way in." In the long run, these will more than probably fall into the n°2 problem section, though.
All in all, I see no drawbacks in instauring a fee. That is, apart from actually making the payment itself!