Yes - it's a potentiometer = a variable resistor.
Cheaper, the potnetiometer costs more than a button and it's difficult to remote control.
Although I have an expensive amplifier where the remote control drives a motor which turns the volume knob.
In theory yes, but in practice there is a limited amount of quality in the audio signal (especially on a TV) so if there is 0.5 units of "noise" then being able to adjust form 2 to 2.5 is a bit pointless. You can always make the digital control to go up in 0.1 unit steps if you like.
Another reason for the digital is that the potentiometer is noisy when it is being turned (at least on cheap ones) so you get a crackle or hiss as you adjust it which people dislike.