Like you already hinted at batteries are DC systems and can only be charged using DC. Many EVs have at least a small AC to DC converter on board. When you plug it into an AC source the charging speed is limited by the size of that converter.
DC charging stations bring their own converters which are oftentimes much more powerful and therefore heavier than what your car carries along.
Whether you use an external 19kW converter or your cars internal converter doesn't make a difference. In both cases the cars charging circuitry will monitor for dangerous situations such as overheating and throttle the charger down if need be.
The important question is how large your cars converter actually is. Sure the L2 charger provides 19kW AC but can your car's converter actually use all of that?
If it can only do 10-15-ish kW then it'll charge slower and therefore won't tax the battery as much as a DC charger with 19kW would.
I don't know what car this is and how PHEVs play into this but existing BEVs have been charging with much higher speeds for more than 100,000 miles and generally don't end up with broken batteries.
Depends a lot on the make and model of course, as I'm sure there are some horrible examples out there. But the public fast chargers wouldn't be under such demand if it was that damaging to the cars.