People who are regarded as overqualified or too old to be hired are the last to be hired - at least by large companies - because the HR people weed them out. They are not working for their company by doing this, however, but for themselves.
Overqualified people tend to get promoted quickly through several successive positions as their talents are recognized. These positions could have been filled with new hires, involving HR - or personnel - much more and perhaps a few exit interviews could be thrown in. Nothing feeds HR like turnover.
With over 15 years to go until retirement, the over-50 set get eliminated as soon as there is a clue in the resume of longevity - a line such as TV repair apprentice would do. Age discrimination must occur early in the process because once it can be proven, it can be illegal. This procedure saves HR folks lots of headaches. Also, preliminary training is often provided by the HR department as a service to the rest of the company. After a couple years of experience - and training investments - younger employees are ready to find another entry for the resume, providing fresh work for HR.
The big system however is, in part, based on employer-provided health care. Some people would not even continue to work if that were otherwise affordable. Passing people into health uncertainty - perhaps as far as Medicaid - for as much as 15 years does the federal budget deficit no good. More unhealthy people entering Medicare is another result. Many people are just starting to shine by 50 and could be a greater asset than a micky-d part-timer or a greeter in the wall. But it just wouldn't make sense for HR.