There is only one real a/d convertor on the chip. It multiplexes the pins that can do analog, so we can exploit that for part of the addressing. Two bits worth, that is one of the four chips.
You need code to take a number 0..15 and set 4 address pins to select 1 of 16 mix channels on every external chip.
Then read across 4 A/D inputs.
The code you write is a single thread, just one thing stepping along, so there is no advantage to using 4 pins for each external chip!
The analogy isn't strict, but think of it like the advantage a loop has over writing almost the same line of code multiple times.
and I cannot think of an advantage to being able to set your four chips to four different addresses, unless you were to say
"sometimes I want to be able to look at 4 different A/Ds only, so I want to, say, pick A3, B7, C13 and D14 and read only them over and over"
But I don't think you mean to need to do that, one, and two, so what if you had to change the single address and do a read four times over?
That is the beauty of multiplexing.
I srsly wonder if you could find an example of someone not combining I/O lines in parallel to address external chips.
But do this if you remain unconvinced:
Write the code for one multiplexer reading one of sixteen pots. It can be done variously between naive and expert, makes no difference in the end. Dunno where your coding/borrowing skills are, but this obvsly needs to be done. We can help of course.
Then say, OK, that's good, now I want to do the other 3 chips.