When you're at a DC fast charger they still only have access to AC power from the grid, but you want 250kw, 350kw of DC power to charge the car. Not only do you need 20x the inverters, but because they don't have to fit in a car and move around, they're fitted with larger, more efficient cooling.
I also heard that it was very noisy during charging.
[1] 80amps at 240v, at least in the US, not sure about the type 2 connector used in EU
[2] code in the US says you should only draw 80% of the rated current if the load is continuous
Most public AC chargers around me are 6.6kw and it's truly a useless amount of power. It's about 20mph, so a 20 minute food stop is giving you ~7 miles of range. To get a 50% charge takes about 6 hours. Even in a 9-5 full work day you're not able to get a full charge.
It looks elegant on paper, at least, but I'm sure there are reasons why it's not done. Maybe due to safety considerations, maybe because the inverter can't handle that much continuous power, or maybe it's just cheaper to have a few big supercharger inverters than to slightly increase the cost of connectors on every car.
Perhaps there are also weight optimizations being made that limit bidirectionality of the inverter.