Not to belabor the math, but the math doesn't lie. It took 14 years to accumulate $100K, likely exponentially saved. With half it gone and chump change left over each month, to reaccumulate another $50 - 100K would realistically take longer than he's likely to own the car, and with aging kids, maybe forever.
I kept reading the OPs post again but I still can't see where the 14 years came up from. If it's an assumption, there could be one on the other end of the spectrum as well. With about $9k going out, I'd assume a good few $k go back into savings so then $50 shouldn't take that long to put back.
Your scenario could be true as well though, in which case yeah, such a huge downpayment on a new car doesn't make much sense.