Look at it this way. Companies , and web masters pay big bucks to target advertising for thier site with the major search engines. Thats the holy grail of a great web page. Targeted links with other similar web pages. Not linier web rings.
Some web rings are just that RINGs.
So what if you have a bummer of a web site on either side of you in the ring. Your not going to get much traffic from them. Also all web rings are not showing folks visiting the other sites a bit of what your sites about. A banner can be a visual magnet. A web ring could never do this.