First, don't worry that powering the CB directly from the battery means the CB won't shut off with the key. There will be many times on the trail where you'll want the ability to leave the CB on without also wanting the keys in the ignition or even in the On or ACC position. But as I said, don't worry about that since the CB could remain on for weeks if not months without killing the battery even if you never started the Jeep. CBs just don't draw enough power to worry about when not transmitting.
Noise-wise, there are just some power circuits that are electrically noisy... circuits that have the fuel pump or alternator on them being two such noisy circuits. Such circuits can introduce whining, buzzing, etc. into the CB's received and transmitted audio. Connecting directly to the battery will give you the cleanest/most noise-free power of any source of power on the Jeep. Not to mention the battery also looks like a big power filter that helps to filter out/absorb noise that may get introduced into various circuits it is exposed to.