Although blade flex's primary role is durability, preventing the sword from bending/shattering/otherwise breaking...
There is another benefit
A certain degree of blade flex will also make cutting easier, because your blade alignment doesn't have to be perfect. This can be seen in test cutting, especially in slow-motion. More flexible swords (like tulwars/pulwar, Grosses Messer, etc.) are generally easier to cut with than stiffer ones (like a Katana).
As with everything everything, there is a happy medium to this property. To illustrate this, think of a sword coming down at some angle (not 90 deg) at a surface.
Too much flex causes the edge to flex when encountering a surface. The out-of-cutting-plane forces bend the blade (so it is no longer aligned with the force of the cut) and results in a shallow or no cut. Think about trying to cut with a piece of paper held on the far edge. It bends before it can do any damage.
Too much stiffness and your entire blade turns as it cuts. Those out-of-plane forces have to go somewhere: the stiffness means the forces result in movement, turning direction of the cut. You'll need to apply a counter force (specifically, a torque or moment, but let's not be pedantic here) or the blade will be stuck, deformed, or deliver a shallow cut. This just makes cutting harder- more force needed or smaller acceptable cut angle!
So having a happy medium is important here. The correct degree of flex allows the out-of-plane forces to bend the blade, allowing the blade continue in the direction of the cut, while minimizing the twist from an off-nominal cut. This happy medium means it's easier to deliver a good cut.
As always, other factors apply, including edge geometry, sharpness, blade cross-section, force applied (drawing/pushing/hewing), and the target itself.