You sound like a Yankee fan's perspective. You make several assumptions and they are all leaning towards making a case for Gardner being worth Bailey for the Reds. You assume Hamilton is a poor fielder (he is a very good fielder) and you said Hamilton has a below .300 OBP (not true) and you mention Bailey having his break out year in 20013 (he actually has been good for at least three years and has two no-hitters) and you say he is homerun prone(He ranked third among the Reds' starters).
The Reds would never take the risk of making a qualifying offer to Gardner. Saddled with losing a draft choice, he might take it, and they'd be screwed. The Reds can't afford to operate that way. They couldn't gamble on an offer to Arroyo, and they wouldn't Gardner.
The Reds are better off keeping Bailey for one year if the return is one year of Gardner. Replacing Arroyo's and Bailey's innings would be difficult enough, but they also have to be prepared to replace Latos (elbow), Cueto (lat), and Cingrani (back).
The Reds will probably go with Hamilton in center. He is their top prospect and they are willing to go through the growing pains. They went a few years with Drew Stubbs in center and leading off and won their division with him there in 2010.
Basically, your suggestion is that the Reds can be better by getting rid of Bailey and replacing Choo with Gardner. It doesn't make sense. If the Yankees are willing to take Phillips and his contract, that would work for the Reds.