There is every reason to require overflows on laundry sinks. With most homes placing laundry rooms on second or third levels today, the real question is why they are not required in the U.S. like they are everywhere else in the world. I know many people who have had the same disaster as you. It takes 10-15 minutes to fill one of these sinks even half way. So it is very easy to be putting away laundry while waiting for it to fill when the phone rings, and the rest is history. Soon it is raining in the den because you were trying to get an appointment for your sick child and all else left your brain.
One doesn't ever leave a bathroom sink while brushing teeth, yet overflows are generally required. And you can hear the thunder of a bathtub all over the house as a reminder. We have never even come close to an overflow accident happening in the bath so we are not careless, but the laundry sink has over flowed three times in 12 years.
You can still find overflow laundry/kitchen sinks ready made in Britain and Australia (Voilamart's is under $150) if you can get them shipped. One US company (JustSinks/Integrasystem) has them, but they are over $650 which is outrageous as they use an Industrial gauge steel. However one $1000 ceiling damage repair might make it all worthwhile.
Good luck. I hope it works.