Why is the electric field due to a charged infinite cylinder identical to that produced by an infinite line of charge?

Maybe it helps to compare your cylinder with a cylinder with a tiny radius, but with the same linear charge density. To have the same linear charge density, the smaller cylinder has to have a large surface density, because its surface per unit length is smaller.

Contours of equal field strength are concentric rings around a single charge (in 2D, spheres in 3D).

So if you instead create a ring of equal charges it's as if you created one of those contours, from outside the ring and in the plane of the ring anyway.

Inside the ring it is v. interesting because there is an integral proof that the summed forces cancel, there is no field strength. This is a starting point for modelling the fairly well known Farady cage.

Fields propagating between the charges neighbouring each other on the ring are summed not lost, so the charges on the ring individually produce weaker fields than the contour.

Comparing the fields of the line and the cylinder, there are a couple of important differences. First, there are differences in distance. For the cylinder, some of the charges are closer to the point at which are measuring the field than the distance to the symmetry axis, and some of the charges are farther away. Because of the $1/r^{2}$ behavior of the field, you might be inclined to believe that the increase in the field due to the closer charge would be greater than the decrease due to the charges farther away. However, this is not the only effect.

The other difference between the two configurations, which weakens the physical electric field, is that the bits of charge "off to the sides" of the cylinder produce fields that are not pointed in the radial direction. Everything except the radial field cancels by symmetry, so the oblique components of the field are effectively "lost." This further weakens the field (relative to what I discussed in the previous paragraph) and the result is a field identical to that of the line charge.