Hi,
Based on my knowledge, level 1 or 2 charging is more complicated because AC should be converted to DC. However, level 3 charging is just using DC to charge the battery.
Somehow my car does not work at the level 3 charging system. (So I towed to a dealership and they told me) level 1 charging is working (and then told me to bring it back).
(who charges at 1~2 kW…)
Is it technically possible for Level 3 charging to fail to work, but Level 1 charging will work?
Yes.
There are control systems that engage the DC charging circuit to allow power to go directly to the battery through the DC charging pins. That is usually a system of relays that have to engage once a connection to the charger is recognized. If those switching relays fail, the communication module fails, or something in the charge port is broken then the car will not accept power from the charger.
Level 1 & Level 2 charging goes through a different circuit with its own logic and onboard charger, so it is definitely possible for one of those two charging methods to fail independently.