Its complicated, is the answer.
Money, experience, risk..
The 'old guys' have got money, they can afford to have a big stable full of young, intermediate and more experienced horses to bring on, and the required staff, including working pupils and stable riders to be out educating those horses in the lower level competitions and bringing them on under their expert eye.
Those horses on the whole do not belong to them - some do, most in part ownership and many wholly owned by someone (or someoneS else)...
Owners put their horses where they are most likely to do well, learn well, compete well, raise their value as broodmares, stallions, or to raise the value of their parents - a stallion and broodmare are rated by the performance of their offspring after all.
So does an owner take a risk on a young rider who only has a handful of horses and can only get to a few competitions, only has perhaps a couple of staff and riders, so if theres an accident, those horses won't be competing but will be standing in stables and fields doing nothing for months?
Or do you send your valuable potential superstar to a big name where even IF the worst happens and two of their stable riders break a limb next week, that horse is STILL going to get out there and compete and get a competition record...
The horse world (and this is the reason I got the hell out after a year at equine college) still lives in the dark ages when it comes to employing grooms, exercise riders, working pupils etc. They are paid a pittance, they are worked INCREDIBLY hard on the basis that they 'do it because they love horses', and thats one reason we have fewer young riders coming up - we still do have a lot of good un's.. but less kids are willing to put themselves through that for the slim chance that they will be the next Charlotte or the next Scott or the next Ben... and the very VERY high chance that they will spend the next 40 years shovelling shit and riding loopers that want to kill you. And then when you are too old and crippled to do it any more, turns out you are too old and knackered and have no transferrable skills to do anything else!
The fact the old guys are STILL at it is a great thing though - they are out there, still winning medals and that means equestrian sports will still get funding from the lottery and govt, and from sponsors and owners - theres still motivation to own good horses, to put them with british riders rather than sell them overseas or give the ride to foreign riders.