An excellent question. In theory, there is no such thing as "too cold" for a freezer, so the low temp. alarm setting seems to be pointless. However, if such a unit does activate a low temp. alarm, it may indicate that the unit is malfunctioning in some way. It might just give you time to intervene before the unit goes "bang". I hope I've sufficiently emphasized the low probabilities of the above happening.
Our facility still checks the low alarm points for our walk-in freezers (-20 C). Luckily, we have access to liquid nitrogen (LN2) which is very convenient and quick. In the past, we've very awkwardly used a sludge of alcohol and dry-ice to get a very low temperature (-60 C), but this doesn't help with ultra-colds (-80 C).
For physical science reasons, we are unable to activate the low alarm on our liquid nitrogen tank !!!! We actually had an inspector challenge us on this issue a number of years ago.