I think we need to be careful to define "Starting" and what it consists of and what ages are "too young" for what parts. For instance, I handle mine several times/day from the day they're born, haul them in the trailer even if it's just around the block several times a month, teach them to halter and lead from day 1. By 6 months I expect them to halter, lead, stand for farrier and vet, bathe, load, ride and unload with no drama. I take them to shows once they're weaned, even if it's only to walk them around the grounds (in hand) and sleep in a stall away from home. I start ground work by the time they're 6 months old, show them in hand from weaners to 2 years and around 18 months start teaching them to carry a bit & saddle, in hand. Once they're 2, they go to the trainer's to be started under saddle. They're there for about 90 days. At least 30-45 days of that is more ground work, ground driving, being ponied off of another riding horse, in hand trail obstacles, getting tied, getting used to cattle, donkeys, dogs, cats, cars, trucks, ATVS. 30-45 days is actually spent having someone get up on the horse and sit. Then walk around in a circle, then trot in a circle (round pen work). Most won't make it out of the round pen in that time but a few do. They start following cows, pushing the cows up from the bottoms (all at a walk and maybe a few trot steps). I try to have this training coincide with cooler weather, so say Oct-Dec. Then after the 90 days they come home and are out on pasture with their friends just being horses and decompressing until spring. Then they go back for 90 more days, so April-June and home for the heat of the summer. In the 2nd 90 days we try to get them independent enough to ride out on the back 500, push some slow cows, maybe start trying to rope a slow cow (they're not roping horses but any training and exposure is good), chase a hot heels at the trot and for the last 30 days lope big, slow circles on the correct lead. By then I expect them to let me clip them if needed, bathe, put a blanket or sheet on & off, no drama.
By the time they're done with the 2nd 90 days, if they're a sale horse, we do video and pics and advertise as a prospect. If they're staying here to be shown, then we keep doing the 90 days home, 90 days trainer until they're 4. Then they go into full time training for whatever their "grown up" job is going to be.
Here's a video of Mort the Minion (Mort) as a 3 year old, 30 days under saddle. He was a very precocious horse, so I held him back a year because I didn't want him pushed. He just never found a reason to say, "NO" to anyone. Following this plan, we have never had a young horse need injections or any other interventions.