Any differential receiver would handle unbalanced signal, just connect the cold input to ground. In fact is a better way to do so, as you can connect the shield directly to the chasis and sense the chasis voltage.
Also, all inputs are differential, you just compare to points to get a voltage, but what you are thinking as unbalanced receiver gets the reference always from ground, and if ypu connect that ground to the amp you have one of three non ideal conditions. A ground loop connecting the shield to chasis and circuit ground at the receiver input, the shield connected to the k put but not the chasis directly or the shield connected to the chasis directly and the sense voltage from circuit ground. Ground loop is a known bad. Not connecting the shield directly to the chasis makes the shield useless to shield RF, and sensing from ground and not from chasis makes a noisy sensing of the input.
A differential input signal will have 6dB more dynamic range than a single ended one, as the input stage must handle your 1V peaks, the differential signal will have 4Vpp amd the single ended only 2Vpp.
Note that balanced and differential are different concepts, and you can have one without the other. For now I leave you with the homework to look for that.
JS