You'll find different recommendations from different manufacturers. That Purina chart uses a combined Starter and Grower which can be used from Day 1 until you switch to Layer. I usually feed the combined Starter/Grower until about 6 weeks, then switch to Grower. My feed store does not carry just plain Starter. We don't all have the same choices. If you have the straight Starter-Grower-Layer progression available, you can feed Starter anywhere from 4 to 8 weeks, just switch to Grower whenever the Starter runs out in that period.
The normal recommendation is to switch to Layer at 20 weeks or when you get your first egg. I have not seen any study that mentioned 16 weeks as beneficial as opposed to the normal 20 weeks. Not that I doubt Fred has seen it. I'd just be interested in the source.
The earliest I have ever had a pullet start laying was 16 weeks. That was from a mutt pullet I hatched from my mixed flock. Normally, out of a flock of maybe 8 to 10 pullets, first egg is around 19 to 20 weeks with about half of them laying by 23 to 25 weeks. I don't switch to Layer until after that first egg appears.
When I have younger chickens with the flock, I feed Grower with oyster shell on the side. This way, the ones that need the extra calcium get it and those that don't need it don't. Occasionally, I'll see one of the young ones pecking at the oyster shell, but that is just curiosity. They don't eat enough to cause any harm as long as they have grit available. If you look at the analysis on the tag, you'll see that the only reallly significant difference in Grower and Layer is calcium. The rest are pretty much the same with just minor differences.
Extra calcium can cause problems in growing chicks. That has been well documented. It is not that it absolutely will cause a problem each and every time, but it can and does. Of course, it depends on how much extra calcium they eat. A few bites of Layer or a peck or two of oyster shell will not be a problem. The two problems mentioned are bone deformation and kidney damage. The bone deformation, if it occurs, may or may not be noticable and may or may not cause a problem. The kidney damage may not be immediately apparent, if it occurs at all. Maybe a year later the chicken falls over dead for no apparent reason. The long term kidney damage finally caught up with it. A lot of times, you just don't know what if any damage was done.
Now I'll muddy the water a bit. This all assumes that the processed chicken feed is all they are eating. If they are free ranging or you feed them a lot of other stuff so they are eating very little of the processed feed, this changes a bit. It is not about the percentage of calcium in the feed that they eat, it is about how much total calcium they eat per day. I'd still not offer Layer to young chicks but just offer oyster shell on the side for those that need it. I free range mine and find that when I have them on the Grower with oyster shell on the side, they eat very little of the oyster shell. They are getting a lot of the calcium they need from bugs and plants they find.
Good luck!