I can't provide the exact reason, but I do believe it was Implemented around 1985 or so that passenger cars (not trucks yet) be equipped or start to be equipped with that additional 3rd brake light, in the center.
Possible reasons:
1. It would be independent of the other 2 brake lights, meaning if there was a circuit failure for the primary brake lights, the third would still work, being activated by hydrolic pressure switch on the brake pedal, vs the standard brake light switch for which many are located right at the brake pedal, and in some cases, can be accidentally disabled or interfered with.. I've seen a number of vehicles over the years where someone got too fussy with their feet/shoes, or a vacuum hose and accidentally disconnected the standard switch. How many times have you been behind a say.. newer Subaru outback or the 2001-2008ish Nissan Altima, and noticed that both primary brake lights were burned out or out, and the center mounted one still worked? (Recalls on both vehicles, FYI, in the case of the Subaru I believe it was just a bad batch of bulbs that burned out quickly)
2. A light at center eye level in many cases is more visible. Think about grille/top of bumper mounted emergency lights on emergency vehicles such as SUVs/Trucks. My Sheriff's Department started utilizing grille/bumper mounted Whelen Strobes on their K5 Blazers back in the 1980s in addition to their Edge bar on the top, which meant that those in cars lower to the ground could see the Grill lights if the emergency vehicle was very close behind them vs not being able to see the light bar on top.
3. Three lights is better than 1 or 2!