I went the direction of private bidders for the following reasons:
1. A few nutty bidders were contacting bidders and buyers on active auctions to complain about me. Complaints to eBay never resulted in any action so that just had to end
2. There was a discussion on this very board about how buyers started figuring out who was who and would track each others activity and buying habits which was unsettling to some (including a few who have bought a considerable amount from me)
3. There were also some disputes which arose where a person leaving a last second bid would get sniped and I would get caught in the middle of it even though they received a proper "you've been outbid notice"
4. On several occasions, I got caught in some weird bid fixing where someone would bid, something would happen and in the last moments of an auction a bid retraction was made reducing the price of an item significantly. Two of the bidders are actually members on this forum. I had no idea what this was about but I don't think it was fair to me as a seller nor as a fellow board member.
As far as shill bidding is concerned, it is just as likely on non-private listings as it is on private ones. I've been out bid on several things only to get an email a few hours later - "hi, just to let you know I have another one exactly like it..." I didn't go for it neither.
If, at the end of an auction, you get a second chance offer, I would think that is fishy too. That isn't right. However, in several cases I've been through (though rare) I will have a bidder who doesn't pay and I offer a second chance or re-list an item. But that's only after a few weeks of trying to sort out the problem.
People get busted for shilling all the time. It sucks but it's been a part of eBay since the beginning.
Edited to Add: If you've been to some country auctions, you might notice there's always a bidder way in the back of the room who randomly jumps in at the awkward moment between "twice, three times...... annddddd, c'mon folks, it's going cheap, and I have xxxx $'s"