Plenty of speakers dip into the 2-ohm range, ESLs often <0.5 ohms, with phase angles of up to around 60 degrees (positive and negative). A quick look through some Stereophile reviews provides lots of data supporting that range. Some amps, tube in particular, also struggle on the other end when impedance goes way high (20~40 ohms or more) even with phase angles below 45 degrees.
Probably not the place to delve into Nyquist stability criteria, root locus plots, and all that jazz... IME/IMO a square wave with a fast edge can be useful to show if an amplifier may have stability issues. In the past I used 1 us edges, so about 350 kHz equivalent (first-order) bandwidth, to look for instability into speaker loads. Most were fine, but occasionally one would exhibit large poorly-damped ringing or outright oscillation.
Analog systems still have wide bandwidth even if digital systems are more band-limited. But higher sampling rates provide the potential for >100 kHz signals intentional or not. This, for me, is less about hearing or musical content (not even a consideration unless the amp is really bad) and just another basic performance test. I have had amplifiers that oscillated ultrasonically and destroyed speakers in the past. Pathological? Maybe, but I don't want to have it happen again... I don't really care to look for music with 100 kHz+ content nor loudspeakers with 0.2-ohm 60 degree impedance spikes; to me it is another of the numerous sort of boundary condition tests I routinely perform on products (RF, mW, mmW, audio...) Steady-state sweeps of sine waves limited to 20 kHz do not represent a worst-case condition to me. As a designer, I am always working to test the worst case and beyond, to make sure the amplifier (or whatever) is stable for any reasonable (and most unreasonable) loads.