Well I guess the question is if Anthias are fed once a day, will they not do well and die? I mean what will happen? Before adding the Anthias I feed all my fish about 5 times a week. I skip every few days to keep my bioload low.
IME, it's a bit more complicated than that. Firstly, the majority of anthias, when they are first imported, are quite skinny, and have lost a lot of their "bulk". Secondly, they are used to eating tiny food items constantly throughout the day. Basically, this means the majority of anthias need to be acclimated to aquarium life in two ways. They need to get accustomed to larger food items, and they need to get used to gorging themselves, and eating MUCH more than they are used to in "one sitting".
Some of the hardy, common species for sale can adapt to single feedings once per day. Of course, this is also subjective. "One feeding" for me means thawed food in a cup being fed once every 30 minutes for several hours

But species like lyretails and bartletts can adapt to gorging themselves. So once they are established in the tank, once a day feedings can suffice. But I wouldn't just recommend this casually to any inexperienced anthias keeper.
And again, I'd have to say, if you are feeding 3 times a day, and the food is gone in a minute or two, and you think this is too much for your tank, then IMO you have inadequate filtration for this size tank/this amount of fish.