The advantages of a latched continuity test are self evident, beyond anecdotal evidence. So it's not just a preference.
Really? You discount the actual use of two types of continuity and the failure of one to solve the problem, while the other did? That is more than "self evident" as it is a real world example. It is not anecdotal, it is an empirical result. Belief does not overcome real world results....
I didn't want to be rude, but I don't believe the evidence presented is actually a valid test. I challenge anyone to reproduce it. If I can rub two perfectly clean probes together without ever breaking contact and get consistent beeps, then I am confident a faulty contact would have beeped as well. I've never heard anyone complain about Fluke's continuity, it's generally considered one of the best in the industry.
Now it is possible the potentiometer he was testing may have been triggering different threshold regions and the two meters might have different thresholds (they probably do), but that's more of Brymen getting lucky than a valid comparison. On a different resistance, Fluke will detect what Brymen won't etc..
Brymen didn't implement some more advanced contact detection method. It's just a non latching continuity test, something Beckman and Fluke improved upon 30-40 years ago.
Fluke 87V's continuity test detects opens or shorts down to a single millisecond. A pulse 3 milliseconds long must have a level about 15dB higher to sound as loud as a 0.5-second (500 millisecond) pulse. Tones and random noise follow roughly the same relationship in loudness vs. pulse length. Something you would never hear out of a buzzer if the continuity test wasn't latching.
There is no question, fast latching continuity test is superior.