While it may not necessarily be true that an older horse will be super calm and super well mannered, and a four year old might...that four year old has what? Two years of under saddle work AT MOST. And depending on the breed, hopefully only a year. Their nature might be very good, they might have been well trained, but how much experience can they get in a year?
Let's look at it like this. Joe Blow got a new job one year ago as a doctor. Many times he has to get another doctor in the hospital to give him a second opinion, because of his short experience. Joe is a great doctor, and very nice, but he just hasn't been in his field long enough to know as much as the older doctors.
The other doctors have more than 10 years experience, and have seen and experienced a lot.
Mark Park, one of the experienced doctors, although he is experienced, is careless and displays rude behavior. Despite his years of experience, he knows quite a bit less than the other doctors of his experience years.
Basically, yes, there are older horses that are NOT beginner fit, but I have never met one 4 year old horse that I'd say is beginner safe. They can be so well behaved, but they are STILL green. Green+Green=Black&Blue. Because the horse after one year of training is still green, still has a lot to learn, they need an experienced rider to guide them and teach them and finish their training. They WILL have green moments, no matter how good natured. They will need a rider who knows how to handle those moments, and how to make it a positive experience.
Cinnamon Whiskey 11 y/o 15hh Chestnut AQHA mare, 2'6 Jumpers