They're not asking you to pay 7 dollars "just to vote". They need to know the opinion of people who are active and willing to pay. I don't have any exact figures, but if you consider how much revenue a single ad impression generates, you should be able to imagine that the larger part of Jagex' revenue comes from memberships.
To keep the server running, they would either need many free players or a much smaller amount of paying players. If they find that many currently paying players would also be prepared to pay for the '07 servers, that would lead them to think that they have a higher income per player for the '07 servers. If more people are interested, they will allow free players to play because the sheer amount of ad impressions will generate a fair amount of revenue.
Another reason is that when keeping voting for paying members only, you can't just make a bunch of new accounts just to vote (and totally mess up the poll results). Paying members are also more likely to be active, enthusiastic and knowledgeable about the game and the community.
This is just how I see things and I might be totally off, but I think what I said is at least somewhat accurate.
14-Feb-2013 00:26:00