Why even bother with such a slow transfer when the 3 day one only requires 600 m/sec more delta V?

When the delta-V is comparable to or greater than the effective exhaust velocity, a small change can have a pretty big impact on payload.

For example, suppose a Centaur (

*I*_{sp} 450.5 s, inert mass 2,316 kg, propellant mass 20,830 kg) is the trans-lunar injection stage. Assuming residuals of 0.5%, I get a payload 18,100 kg to 3.1 km/s but just 13,500 to 3.7 km/s. In other words, lowering the delta-V by 13% increases the payload by 34%.