You're ignoring the important point of showing the student that a varying
charge density along the surface of a cylinder can produce a field in the
interior. It's important to show this (it's Fig. 19.19, in the middle of
the discussion you're talking about, where potential is not mentioned),
because in the earlier chapters on electrostatics students did not
encounter anything like this. The demo program I posted supports this: a
line of charged rings whose charge varies linearly along the line not only
produces a field inside but one which is quite uniform. This is of course
far from proving that the surface charge on a simple single loop circuit
has this pattern, but the contrast is with a loop that has something like a
uniform charge density, which is the kind of charge distribution
encountered in electrostatics.
Even a real battery (which we deal with in some detail in chapter 20)
maintains both a potential difference and a charge separation, with the
sole exception of it being connected to a circuit of zero resistance, so I
don't understand your point.