OK Folks, STOP saying that! Some of you may have bees that WILL stop taking it, Some dont! I have both!
Some of the older hives will stop taking syrup, but not all of them. My external feeder goes from having six layer deep bees trying to get to the syrup on each others backs during the early spring, to ONE layer of bees that still takes 5 gallons of syrup in a day during the best part of the flow.
IF.. I continue to feed, those hives/bees that continue to take the syrup would, and will backfill the brood nest until they either dwindled or absconded..
Feeding with jars, and using three tiny holes in the jars helps this situation, because they cannot get enough of the syrup fast enough to backfill the cells.. PROVIDED there is no flow..
IF there is an excellent flow, AND you are feeding, even with few holes in a jar type feeder, they will STILL backfill the brood nest... This is one of the reasons you inspect the hives, to insure they have room to lay.
If you have comb to draw, have a newly started hive, or are building up for spring, feeding is the thing to do. If you need them to put away stores for winter, feeding is the thing to do. More than once, I have inspected a hive to find it "nearly" plugged out with syrup.. I shake out the frames that are supposed to be brood nest, and remove what ever the source of the syrup is.. Sticking that comb into the freezer and replacing it with a drawn comb is a viable option.. if it is natural flow, there is not much you can do, except attempt to shake out the combs so the bees will clean them, and with luck, allow the queen to lay in them... Usually, a natural flow that good only lasts a short time before it trickles back to normal, so its just a matter of keeping an eye on how much they are storing..
It only takes losing one hive because they backfilled themselves out of room before you too will start paying attention, and stop saying...
Feed till they stop taking it!
Just my experience, with greedy bees...