I feed an all-in-one type feed to pretty much all my birds, hatch to butcher, males, females, everyone.
I have changed to medicated starter for some of my brooder babies because of how wet and warm our winter was, I'm sure my ground is teeming with cocci this year. It's been an issue on and off in the past, and I have a feeling this year will be a banner year for it here. But that's the only reason for the separate starter, in dryer or colder years I've just given everyone all in one and they do fine. Oyster shell and egg shells for the layer hens, no one else is interested in them.
x2 Kind of depends on your purposes too and your particular flock and environment conditions (which can change from year to year).
All flock is meant to be a feed for mixed flocks, typically from age 7 weeks and older to layers (with calcium supplement) and roosters. Five weeks of age is likely close enough to switch to all flock. Compare your feed labels as products vary between companies. Typically chick start contains a lot more vitamin and mineral supplementation for growing bodies. Chick Start will be around 18% protein, also important for growing bodies. Most all flock is 18% protein, but as stated most all flock does not have anywhere near the vitamin/mineral supplementation as chick start.
Breed types and environment conditions then can factor in. If you have commercial hybrid layer types that mature faster (often laying by 22 weeks), switching out earlier to layer is not necessarily harmful. There are studies indicating feeding layer to commercial hybrid layers who mature earlier is beneficial as they need the higher calcium since they will be going into production sooner. Although you don't want to push them too quickly into lay as that can cause problems with the egg duct too.
If you have more heritage type breeds that mature more slowly, you may desire to have them on a chick start longer to give their bodies time to mature with the additional nutrients found in the typical chick start. That may not be an issue for most breeds wherein all flock suffices (albeit I think it may also be more convenience for the flock keeper than nutritional targeting). You could also supplement with a vitamin/mineral product if you chose. Rooster Booster produces nice products for that type of supplementation. The big thing is the calcium. As stated in this thread, young chicks cannot handle calcium well. Roosters can handle it for a time, some better than others, but the general consensus is they are better and longer lived without the additional calcium clogging their internal system...although many a rooster seems to have survived well enough on layer, so you will get mixed reviews on that issue.
All flock usually comes in a choice of pellet and crumble. Chick start, at least in my area, is crumble only. Pellet produces less waste than crumble (which I find crumble goes to powder way too quickly), but pellet can be more difficult for younger birds to eat. If you find your hens are laying thin shelled eggs on all flock (my problem with some all flock), you can switch from oyster shell to calcite grit as sometimes that is digested better (in my experience).
So for most flock owners who desire to avoid calcium overload with those birds who do not need it, all flock has been a good feed choice. But watch your flock and consider your goals. If you want to grow certain birds to optimum, it is usually best to use a feed that is targeted to their type. My daughter went through Vet Tech school, and we learned there is a lot of science behind those commercially produced feed formulas. Our Guide Dog program also commented and focused on appropriate nutrition for the particular breed type. Targeted feed can make the difference between a pathetic 3.5 to 4lb meat bird and a beautiful 6 to 8lb tasty roaster. If you are in an area with low sunshine or extreme weather, you may find your birds need better supplementation for vitamins (D) to thrive. Vitamin deficiency definitely causes a multitude of issues and conditions from wry neck to odd gaits.
All said, many utility flock owners do just fine on a general flock food adjusting if they see issues arise that are linked to nutrition (poor egg quality, poor development, lack luster feathers not attributed to parasites, wry neck, leg/gait issues, poor hatch rates).
That covers the basic concept of nutrition; now your thoughts on medicated feed. The reason for medicated chick start as I am sure you know is to prevent Coccidiosis...the dysentary like disease that occurs when there is an overgrowth of coccidia (a protozoa) in the gut of an animal. Coccidia live pretty much in all soil everywhere and are not a problem until there is an overgrowth as most animals keep it at bay with their immune system unless their system is compromised (from parasites or illness). If a bird has a compromised or undeveloped immune system (as in young birds and birds stressed from travel...your newly purchased older birds), an overgrowh can quickly occur producing the illness of coccidiosis.
Not all Coccidiosis produces bloody diarrhea as it depends upon where the coccidia take up residence in the gut. Often your first and only symptoms are a lethargic, huddled bird, with an internally withdrawn look about them. Then if the load is located low enough in the intestinal tract (as commonly happens) you will see the classic bloody diarrhea. By the time you see that, the bird often is fatally ill, and it is harder to help them recover as they will not eat or drink. To prevent that severity of condition, preventative measure is taken through medicated feed. Amprolium is the medicine provided in medicated feed (the same med in Corid at a higher dosage for crisis and acute treatment). Amprolium in medicated feed is given in very low dose so that it hinders the growth of the coccidia (through hindering vitamin b absorption thus starving the protozoa) but allows some to grow so that the bird slowly gains an immunity. That is why it is fed until the bird is close to maturity and thus mature immune system. This immunity can be lost as stated from stress or anything that compromises the bird's immune system. Also this immunity is only for the strain the bird was exposed to...and there are many different strains of coccidia. Moving a bird from one area to another (as in purchase) can both shock the body lowering the immune system and bring it in contact with a new unfamiliar strain. It is also why you need careful bio-security so you don't track the mud from Farmer Jones and his strain of coccidia to your backyard.
Another situation is when weather or environmental conditions create an overload in the soil. This occurs with warm, moist conditions and causes a build up of the oocyts (the spores of the coccidia). This also can occur from continuous use of a coop. Oocyts are hard to get rid of, and if you have not had a good killing freeze during winter (which only scales the population back but never elminates), nor disinfectants periodically with litter removal, you can have a population explosion that overwhelms even healthy systems.
Why all that information? Because the answer to use medicated really depends upon your environment and flock. I always put feed store and newly purchased birds on medicated feed as they have had both travel shock and a new strain to contend with. I avoid putting broody hatched chicks on medicated feed as I have had problems with the chicks becoming vitamin B deficient on the medicated feed (exhibited by toe walking and leg deformities). Last summer I had the worse ever outbreak of coccidiosis after uncharacteristically unclean coops (family health emergency had prevented my normal chores) and unseasonably warm, moist weather. (shout out to @donrae I had that here too up North from you). I am now as a matter of fact treating all chicks with medicated feed to keep the oocyst load lower as I continue to remove litter and clean coops waiting for a really good killing winter.
Oh...Edited to Add...it is a myth that Amprolium based medicated feed is bad for layers. I have read numerous studies and the latest government regs allow for a certain amount of Amprolium based feed because coccidiosis is a problem in the commercial industry (with all those birds in close quarters). You can feed medicated chick start to layers and eat the eggs.
Long response. Hopefully that explains "one size does not fit all." Research and do what you feel is best for your flock.
LofMc