if it was 1A into 8 Ohms, that's 8W.  2A into 4 Ohms, that's 16W.  if
your output is limited to say 30W peak, trying to suck 60W out of it
would be a massive problem that'll fry semiconductors quite nicely!
especially in a nice hot car where the output heat sinks are crammed
into a nice airtight little socket in the dash.  semicons are just not
abuse tolerant.

yup.  the plastic packaging on the output transistors melted and the
circuit board had gone from green to brown in the heat zone.

There are some issues that are less than obvious here. Power TO THE
SPEAKERS is not what counts, power dissipated in the amplifier is the
problem. Contrary to what one might think, power dissipated in the amp
is not at a maximum when power to the speakers is at a maximum (volume
cranked to max. (ours goes to 11)). It occurs when power to the speakers
is at about 40% of max. (Assuming amp output impedance is much smaller
that speaker impedance)

One might say that a dead short is also just an impedance mismatch, and
a dead short certainly can fry an amplifier. Furthermore, in car stereos
you usually don't have *matching* impedances. The output impedance of
the amp is usually quite low compared to the speaker impedance. Thus the
power delivered to the speakers will theoretically increase as you
decrease the speaker impedance until it reaches the amp output
impedance. As a practical matter, things will start to smell foul long
before the speaker impedance is low enough for an impedance match.
Given an amp with x ohms output impedance, max. power should be with
speakers of x ohms as well, but this is not really the design criterion.
Rather, given speakers of 4 ohms, max. power is obtained with an
amplifier output impedance of 0 ohms.

In video and RF, impedance matching is important to avoid reflections.
However, as a rule of thumb, if your cable is shorter than 1/4
wavelength, you don't really care. For audio, that means that your
speaker cables can be up to a mile and a half before you have problems
with reflections (assuming 20 kHz and signal velocity in speaker cable
of about 2/3 the speed of light in vacuum)

To compound the issue, home stereos usually have ample cooling;
Ventilated chassis and large heatsinks, sitting in a room where the
temperature is comfortable for humans. Head units in cars are not at all
well cooled. They are hidden inside the dash where there is no air flow
and in a car that might have baked in the sun all day.

A well designed amp will be short circuit protected and have thermal
shutdown, Even then, if it spends any amount of time close to but not
quite at the trip temperature for the thermal shutdown, it will have a
reduced service life.

Did the wrong speakers kill SaraKat's head unit? Speakers with less than
4 ohms impedance are unusual, and car stereos that can not handle 4 ohm
speakers are unusual as well. Perhaps several speakers were connected in
parallel on each output?