There's an art to giving good concrit and if you have an open community (and I presume that you don't want to face the inevitable wank that will arise if the community is closed) writers who post will have to be prepared to accept and respond to criticisms from anyone who has something to say, even if the criticisms are unhelpful or beside the point. It could be very confusing for some writers, and also time-consuming.

On the other hand, those who don't want public concrit won't join, and those who find it an unsatisfactory experience won't post again. Perhaps you should conduct a poll to find out how many people want public concrit, then take it from there.