You don't necessarily raise the noise floor with a hotter input, but I know what you mean because it may force you to attenuate the input.Not sure u will find a dac that outputs 6v , because it’s not needed , an amp only needs some much input voltage, any higher and u raise the noise floor , the amp should be boosting the signal , not the device .
In theory, it would be best to have higher voltage line outputs and low gain amplifiers. You do see this more in pro audio. Not a really big difference or issue though. Main thing is to avoid amplifying - attenuating - amplifying in most cases as you probably know.