Actually, i think the sound quality differences between different plugs is negligible, and certainly not the reason why they were designed like that...
Headphones were most common in recording/radio studios, where durability/ease of changing plugs is most important. So the 1/4" plugs gradually caught on as the standard in all audio equipment.
But when portables came around, they couldn't fit the large jack into the players, and the large plug was inconvenient. So they switched to the smaller 1/8" jacks. These are less durable, and very inconvenient for studio use, but they are better for portables...
The surface area doesn't have any (audiable) effect on the signal. The actual contact area is like <1mm thick, so a difference in surface area will have no effect on the overall conductivity of the headphone cord. But If there is oxidation or somthing on the plug, a plug with a larger surface area will be less likely to develop intermittancy problems. So you could say the 1/4" plugs are more reliable, but they don't sound better...
(and almost all high end headphones use the 1/8" plugs so it's pretty safe it does not degrade the sound quality...)