> In the places I have seen it used, the 'arbitrary' column typically has the same value for the entire group, e.g. for efficiently selecting distinct texts based on their hash values.

I agree that case is convenient. But I've seen it being used to actually pick a random row, where a different row would have a different result (such that the output of the program would definitely be different), and it's clear the developers who wrote it didn't fully understand this was going on. I wrote it up in a report for this particular client but they didn't seem to want to touch this particular very old and venerable code.