Why is the characteristic impedance usually purely resistive?
Do you think characteristic impedance is purely resistive because it is normally labelled as 50ohm or 75ohm and not in the form a + jb?

If so it means you are confusing transmission lines with conductors and characteristic impedance with regular impedance 

Take an infinitely long line of perfect (no loss) two-line conductor, it will have ZERO resistance but can be 50ohms. The reason is ANY transmission line must have both capacitance (insulation between conductors and voltage difference makes a capacitor) and inductance (current charging the capacitance induces magnetic field which stores energy)
as shown in this picture
But how does this look like some finite non-complex impedance like 50ohm?

To DC voltage this transmission line looks like a short circuit, but to AC signals:


The parallel capacitance will cause a splitting of current, which is equivalent (as far as ohms law) to a parallel resistance
The inductance will prevent infinite AC current which is equivalent (as far as ohms law) to a series resistance
In both causes there is no loss! just an impedance that LOOKS resistive
You'll notice that is you buy a cable for RF signals it specifies a frequency at which it LOOKS like 50ohm, this is because the cable is designed such that the capacitance and inductance of the cable resonate and effectively cancel each other out leaving only the effect they have on ohms law meaning there will be an apparent resistive value which is chosen for best power transmission; usually 50Ohms
In such a cable if you input a frequency higher than its rated frequency it will appear inductive (complex with a positive imaginary term), if you input a frequency lower than its rated frequency it will appear capacitive (complex with a negative imaginary component)


Hope this helps, leave a comment if you want be to elaborate further 

source: junior RF electronics engineer, MEng Electrical and Electronic Engineering (2016)