This is not a true statement. There is nothing in Layer feed that will hurt the rooster. Mine has been getting layer feed for the past 7 months and I know others that have fed layer feed to the rooster for 20 years with no adverse affects.
I personally am now feeding a home mix, but not due to the rooster, but changed the entire flock. Hard to separate feed rations when they share the same coop.
I'm sure plenty of people do it with no problems but the biggest thing I've heard against it is too much calcium. Sure there's no actual ingredients that hurt them but there is calcium in excess and unbalanced calcium phosphorus ratios. Maybe for roosters it doesn't hurt them but it sure hurts chicks and I am sure some roosters have suffered or it wouldn't be stated.
As for the last bit about how it is hard to separate feed rations when they live together.... that is very true but that's exactly why some people just feed All Flock/Flock Raiser or a good starter/grower or grower feed with free choice oyster shell (calcium) for the layers. That DEFINITELY won't hurt them.
I don't know, in my opinion I'd rather feed starter/grower or All Flock with oyster shell than risk any potential side effects with the roosters or chicks. Which you may not even noticr until they start aging.
Although fortunately I don't have any roosters or younger chicks and probably won't until I move.