I'll confirm what Joe is saying. Every vehicle I own uses breaker point ignition (Ford trucks excepted) and I don't have any trouble with them. They all get used regularly as normal transportation. I buy NOS point sets whenever I can, although I've had decent luck with Standard Motor Parts Blue Streak points.
About 10 years ago I had a problem similar to yours in the Galaxie and changed the points and associated wiring and still had the problem. It turned out to be a worn distributor shaft. Installing a rebuilt dizzy cured it right up.
More recently I had brand new condensers fail soon after installation (less than 1500 miles). I purchased solid state condensers from Jon G (a member of this forum) and installed them in all my vehicles.
https://www.stovebolt.com/ubbthread...16/re-the-newest-condenser-update-8-2024Everything has been hunky dory since. No need to switch to HEI unless you really want to.