Does merging the chip and the contact pad in a chip-and-pin card make the whole module less reliable?
mechanically, you're nearly right – think of it as top-bottom:

Place the contact pads upside down on a plane surface. Take a bit of (relatively elastic) glue and fix the die onto the center of the contact pad's back. Then use an automatic bonding machine to weld small wires from contact pads to die, with a bit of a "curve". That way, your die gets a bit of mechanical "freedom" from the pads.

Then, go ahead and bend your card. The hardest part to bend is actually the contact pads, the rest is soft plastic. Hence, the deformation at the center of the contacts isn't that bad.