The calcium in the layer feed is hard on the roosters organs. I can't off hand remember which organs but someone may be able to add that info.
I feed chick starter to my hens/flock/roosters; I have tiny Old English Game Bantams and I normally hatch throughout the year so it just makes everything easier to have a smaller sized crumble that suits everyone. I consulted the feed consultant and my vet...and the only thing the vet said is the extra urea from the higher protein will be excreted in the bedding and which would be more of an issue in the winter. In my case I also feed grains so averaged out all my feeds should be close to the acceptable range for protein. I also find they feather better in the fall when they're molting.
If I just had large fowl, and introduced my chicks later...I'd probably opt for a grower/finisher since that feed is not (usually) medicated and give the girls oyster shells free choice in a separate container. Grower/finisher is usually around the 15% mark for protein.