Is there any benefit of making lamps with high wattage LEDs but low wattage driver circuits other than cost?
The LED power may be limited by thermal considerations. Both the power supply and the LED are prone to failure. The former because of possible shoddy transient protection and inevitable death of filter capacitors (exacerbated by the typical high temperatures). LED life will also be greatly foreshortened by high junction temperature. 

These things are a trade-off. My suspicion is that the LED rating of 3W you mention is not really achievable (with any reasonable lifetime) in the environment of the light bulb, and everything (driver and LED) is really close to the line. Here's a snippet from a Chinese "3W" LED datasheet: 



The Power Dissipation is absolute maximum 3W at \$T_A = 25°C \$. It will have to be derated above 25°C at the bulb, so I think you can see that calling that thing a "3W" LED is somewhere between irrationally optimistic and an outright lie. While the bulb maker might be perfectly happy to run it right at 3W, if they die so fast that they are getting 40' container loads of lamps dumped back at them, they'll not be so happy. 

The only thing I really expect to be true of the bulb is the (initial) lumen output (you can expect them to fade over time). If the lumen output falls short, especially out of the box, that is false advertising and I would return them. So far, from reputable makers such as GE, I have not been disappointed. I can't directly measure lumens, but I use lux meter to check light levels on work surfaces and so on, and can reasonably well compare halogen and LED bulbs with similar angles.