I would guess points burning up is some other problem OTHER than bad points, here are some check points, LOL pun fully intended
BATTERY CHARGING VOLTAGE. Running, battery voltage should be 13.8--14.2 with engine warm, in no case above 14.5
COIL could be bad. Check coil running voltage. This varies greatly, might be, idling, anywhere from 10-12 volts but in no case more than 12. Typically less.
SUSPECT bad condenser. Check that the external condenser is hooked to the POSITIVE coil connection, and that the distributor wire is hooked to the NEGATIVE coil connection. The external condenser is for radio suppression
SUSPECT points gap. If the points are set too close, they will burn. Check with a dwell meter. ALWAYS set points "on the wide" side as they will wear closed. Always set timing towards "more" advanced because as the points wear "shut" timing will retard. Always put a tiny tiny amount of hi temp lube on the points rubbing block on the "approach" side. Points, back in the day when "points" were "real" came with a tiny capsule of lube.
MAKE SURE your feeler gauge is clean, and again, set with a dwell meter. Hell, I never even used to USE a feeler. I used to estimate gap, set them with a dwell meter (scope) "on the starter. Then I'd start it up and recheck. They would change some between "on the starter" and running, but after you did this a few times, you knew how much to "adjust." Back in 70--74, I set hundreds and hundreds of 'em