Squiffy,
If a jet did a go round behind a twin "late to vacate" then it ain't got nothing to do with the CAGRO: the jet crew stuffed it up, plain and simple. Don't blame the CAGRO for that. Perhaps the "light twin visitors from the East" DO need a tower...
You say the CAGRO "ends up complicating the situation". After my many times there with and without the CAGRO, I disagree, and things would be chaotic without him/her (onya L), especially if it was only a Dick Smith "I don't have to talk to any $rick" yank CTAF. And I can tell you what: a tower will cost you a fortune, AND you'll get more delays than now. Sure, the CAGRO may need a bit of fine-tuning, but in my extensive experience there, they are pretty good, and don't get in the way. No calls between aircraft are required at all until it actually gets to the separation/sequencing stage: you get the traffic picture in one fell swoop with no fuss.
What's needed is a bit less verbal diarrhoea by pilots (why do some jet pilots call at 15nm when they are joining on downwind??) and the system will work well.
Also, re "several large aircraft movements and a quintillion light aircraft movements per day": very few of the RPT flights are in the air at the same time, and those that are can quite easily manage the situation.