The alternator is wired wrong & possibly bad as well.
The wrong coil, ballast resistor, etc won't kill the points in 20 minutes of run time. 12 volts will kill them but it takes a lot longer than that to kill them & it's starting and stopping that does the damage.
My guess is your alt is being fed straight from the coil with no diode to prevent backfeeding. It's either burning them at shutdown because of that or you're backfeeding the coil way more than 12 volts from that alt.