There are a few things to consider:
Would users who created content be charged for their accounts? I think it would be ludicrous to ask those who bring traffic to the website to pay for its use. If creative minds are exempt, then how would the system account for the hundreds of others who don't necessarily make Flash animations or audio, but who instead organize community events and contribute with advice on the forums.
Would the membership be mandatory? As mentioned above by kaywire, if there were an incentive for a payed membership like a monthly magazine and paying members only area (which would also justify the cost of the membership) and there was still a free membership for those who didn't want any of the extras, that would be fine in my opinion.
Would content creators make more money? Going back to the idea of there being only payed memberships, would content creators get a larger allotment of money through revenue share? Newgrounds would have to recognize that there would be no paying subscribers without the entertainment they come to see.
Would it be worth it? How would charging for memberships improve the site? Obviously, if there were two types of accounts, those with the paying accounts would feel a greater allegiance to the site and this would strengthen the community, however this would cause a rift between the two account type holders. How much traffic would NG lose because of this and how much drama would happen?
A one time fee might be okay, right? I read an article on Cracked recently about internet personalities, blah blah blah, but they mentioned that some sites charge a one time registration fee of ten dollars. The point is that trollers and alts are less common because they won't go through the trouble of paying ten dollars just to fuck with people.
There is a lot to think about, but I for one would pay Newgrounds money if they mailed me a magazine every month and had a special section for payed users where we could talk about how much better we were than the free users.