Tesla said being able to charge a Lithium battery within minutes is possible. The technology is there. It would take serious cooling, though. And of course it would take serious power (around 1 megawatt). Both these things are hard to realize. Building a battery pack with a cooling system that dissipates 100-200 kW of heat is quite a challenge. Getting a megawatt of power is another challenge. Last but not least, the cables would be too heavy and thick to handle. So there are practical limits.
I always hoped that Tesla would come out with an updated Firmware that would run the battery cooling system at max capacity and thus enable faster Supercharging (staying at 120 kW for a longer time). I noticed that even when Supercharging in 100+ degree weather and full desert sun, the battery is cooled just using the radiators and fans. The AC unit does not kick in. If I turn the AC on manually, I hear the cooling fans run at a slower speed which indicates the AC unit provides better cooling. At one public meeting either Elon or JB said Supercharging is actually pretty conservative. They could charge faster but they were unsure about the long term effect on the battery and wanted to stay on the safe side. Tests with Leafs showed that fast charging vs normal charging makes only a small difference in battery aging. And the Leaf doesn't even have any battery cooling at all. I still have hopes Tesla will eventually allow a less conservative Supercharging profile resulting in an overall faster charge speed.
Here is the video (from 2 years ago) where Elon says that Supercharging is very conservative: Elon Musk Townhall meeting Amsterdam (HD): Firmware Version 6.0, SuperCharger Locations Europe, etc. - YouTube
I always hoped that Tesla would come out with an updated Firmware that would run the battery cooling system at max capacity and thus enable faster Supercharging (staying at 120 kW for a longer time). I noticed that even when Supercharging in 100+ degree weather and full desert sun, the battery is cooled just using the radiators and fans. The AC unit does not kick in. If I turn the AC on manually, I hear the cooling fans run at a slower speed which indicates the AC unit provides better cooling. At one public meeting either Elon or JB said Supercharging is actually pretty conservative. They could charge faster but they were unsure about the long term effect on the battery and wanted to stay on the safe side. Tests with Leafs showed that fast charging vs normal charging makes only a small difference in battery aging. And the Leaf doesn't even have any battery cooling at all. I still have hopes Tesla will eventually allow a less conservative Supercharging profile resulting in an overall faster charge speed.
Here is the video (from 2 years ago) where Elon says that Supercharging is very conservative: Elon Musk Townhall meeting Amsterdam (HD): Firmware Version 6.0, SuperCharger Locations Europe, etc. - YouTube