Resistance doesn't change if it is AC or DC. It is just pure resistance. Thus the term "DC Resistance" is a bit of a misnomer. Resistance just doesn't change with frequency, the definition of Resistance.
When it changes with frequency, it is Impedance.
Impedance is the combination of resistance and the reactive component. That reactive component doesn't use any power, but makes driving it more "interesting," which could be called "difficult."
Impedance can be given as a simple number, as in 32 Ohms, or it can be broken out in the two components, or the complex term, as in 30+j9 Ohms. This is a more descriptive way to show Impedance. Keep in mind that in the first case, it is a "nominal 32 Ohms" and it changes with frequency. In the second case, the Resistive component doesn't change with frequency (in headphones), but he reactive component does, so it also only applies at one frequency.
Impedance changes with frequency because the reactive component becomes higher as the frequency increases. If the reactive component is capacitive, it will decrease as the frequency increases. If the reactive component is inductive, the reactive component increases as the frequency increases. Headphones are inductive, as they are made up of COILS, which are, by definition, inductors.
The exception are electrostatic headphones, which can become kind of interesting.
If electrostatic drivers are directly driven, they are going to have a very high series resistance, and will be highly capacitive. This just isn't going to happen in real life, because the Voltage needed to drive them is going to be incredibly high. In the good old days, we sometimes removed the output transformer and allowed the plate supply on a tube amplifier also energize electrostatic speakers and removed both the input transformer and energizing circuits (High Voltage power supplies), and use that high Voltage of the amp to directly drive the speakers.
Headphones have additional safety issues, so I might not want to have 250 to 500 Volts DC right up against my ear!
So, we tend to drive electrostatic headphones (and speakers) through a step-up transformer to increase the Voltage. The good news is they require very little current, so the transformer doesn't require a lot of power.
BUT, a transformer is incredibly inductive, so even electrostatics are inductive in practice, just like dynamic drivers.
In order to make the reactive component less meaningful, we can either use a matching network (not practical for headphones) or we can just drive the headphones with a much lower impedance than the impedance of the headphones. This works great.
Also, while this isn't nearly as important as in speakers, especially the bass drivers in speakers because the coils tend to be very large, the low impedance will absorb the Back-EMF from the driver, preventing it from ringing -- or "damping" it. This was the origin of the rating of "damping factor" which used to be an amplifier specification.
Now days, even with OP AMPS, the impedance of the output stage is very low, so it is nothing to worry about. Even better is when the OP AMP drives a pair of transistors or FETS. The Impedance will then be much lower that 1/10 of an Ohm, in properly designed amplifiers.
I will grant you that some design compromises are often made in very small portable amps, to save space and prolong battery life.
In other situations, matching the output to the load is important. We can waste power in audio, but not in RF applications. Broadcast transmitters (or pretty much any transmitter) work better when matched to the load. In FM broadcast, it is ALWAYS 50+/-j0. In AM broadcasting the tower is NEVER going to present a 50+/-j0 load, so a matching network is used to "bring it in" to 50+/-j0.
