the contact point burning out leads to two things to inspect.
very low impedance ignition coil without resistor is installed
the installed capacitor in the low current circuit is faulty.
If your car is not picking up speed like it should, inspect and adjust the following
dwell angle - this is set by moving the point assy towards or away from the cam in the distributor - the ideal gap is 0.45mm - a sliding fit not dragging.
the contact points should be degreased of its dressing prior to installation.
the centrifugal advance mechanism should be free to move
the vacuum advance plate should be free to move too.
verify the ignition timing by a strobe light with main vacuum pipe removed from advance diaphragm.
It will function normally after that.
lastly let me point out that it is not a CDI system its called a breakerless ignition, it uses a pulse generator and ignitor to switch on/off the ignition coil.
A CDI system actually uses a capacitor in the system to energize the coil.