Are very low impedances really that hard to drive?

In a word, yes.
If an amplifier cannot handle 1 ohm loads then either the protection circuit will cut in - and distort - or the amplifier will clip or worse, overheat and blow a fuse or transistor(s). If you are lucky, the 1 ohm may only appear at certain frequencies which means that an amplifier will not be continuously subjected to overloading, and if the protection circuitry allows transients it might only impact the PSU and power for the duration of the effective pulse.
 
The rule for a transistor and a fuse is . . .
the transistor blows up to protect the fuse.

It does happen to some well engineered amplifiers, that are abused by the owner trying to take an 8 Ohm rated amplifier, and loading it with 1 Ohm.
Part of the problem is the fuse is in the primary, or immediately after the secondary. The rectifiers are followed by a 30,000uF cap (lots of transient current capability to send to the transistor until it blows up).

Everybody seems to want a super stiff power supply, but they will not put a fuse supplying current to the transistor because that will raise the intrinsic output impedance (before global negative feedback is applied; and given a certain dB of negative feedback, it also raises the negative fed-back output impedance).
And then they do not want to put in a protection circuit to protect the amplifier output against those who use 1 Ohm loads, or worse yet, short the speaker leads by mistake.
All of these factors are not present on every amplifier . . . but it does happen sometimes.

Recession: your neighbor is out of work. Depression: you are out of work
Compare that logic to your neighbor's blown amplifier; versus now your amplifier is blown.

I have seen a TO3 Hitachi a MOSFET with a hole burned through the metal cap of the TO3!
 
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"Zobel network is RC."
Zobel defined a network which provided a constant impedance, effectively just R, and that could require the use of inductors or capacitors.
Inductors are often spec't for amps when using electrostatic speakers, and are just as much "Zobel" as the RC used to tame inductive loads.
 
Hey don’t go there! Irony is that class D in general does not blink an eye with difficult loads.
There is no instantaneous current limiting in a class D amplifier. The current can’t rise instantly anyway, - di/dt is limited by the filter inductor - even into a dead short. Any average current limiting scheme takes several pulses to kick in. By then the event has passed. But overall power losses go up like a hockey stick above some point, and if the heat sinking or power supply cant handle that you’re in a different kind of trouble.
 
There is no instantaneous current limiting in a class D amplifier. The current can’t rise instantly anyway, - di/dt is limited by the filter inductor - even into a dead short. Any average current limiting scheme takes several pulses to kick in. By then the event has passed. But overall power losses go up like a hockey stick above some point, and if the heat sinking or power supply cant handle that you’re in a different kind of trouble.
In class AB amplifiers, is it possible for the current to rise instantly?
 
No, but it can rise faster than it can in a 20 uH output inductor. And since the frequency is audio and not the carrier, it can stay ON and continue rising, to higher values, for a longer period of time. Time is the enemy. The SOA is square, for sufficiently short pulses. 10 milliseconds at a time, it’s not.