I don't know about other AE speakers, but around here, the phrase is being thrown around right and left for businesses and organizations that are having to close temporarily because they had Covid-19 cases.
The shtick goes like this: A few Covid cases turn up, other co-workers have to quarantine, visitors have to be contact-traced; and then the director or owner innocently says to the press, 'We have no idea how these cases came to happen, since we have been following all precautions, but nevertheless, out of an abundance of caution, we are closing for at least a week.' It's also usually followed by extreme surface disinfecting, as a show of zeal, even though we now know that droplet / aerosol transmission, and lack of ventilation / distancing, are much more likely to have been the culprits.
In these cases it seems to me to be a cowardly euphemism that really means 'We obviously slipped up, but we have no idea how, and anyway, we don't dare admit it, because there could be liability involved.'
So 'abundance of caution' really means 'We don't really think it should be necessary to close, since we thought we were already doing enough. But since the health department is requiring / recommending it, we see no other choice.' It's actually a denial of culpability / responsibility.
>>dafür häufig "als reine Vorsichtsmaßnahme". Das zeigt an, dass es zwar einen Grund gab, dass die Lage jedoch nicht ernst ist und dass man daher alles richtig gemacht hat. ;-)
Sounds perfect to me. /-: