So Bjorn had a video where he was at Nokian testing winter tires... And while there, he was talking about the DC charger they had there. I think it was a Chempower unit, but it was basically what you described... It connected to AC, tho in this case I think it was 3 phase AC. But anyways, it was able to provide 14 or 16kw DC charging... (I forget the exact number, for simplicity sake, lets say 16). He pointed out the problems with this... He said even tho on paper, 16kw sounded great compared to regular AC home charging... He showed that the Tesla was pre-programmed so that when you connect it to a DC charger, it will always try to precondition the batteries... So in this case, he plugged into the 16kW charger, and he showed that it was using about > 8kW just to warm the battery, and showed that only 7kW was going into the battery. He was saying that his regular home L2 charger actually sent more juice to the battery. He said it would be nice to be able to disable warming that battery, if the DC charger is relatively low power like this, but you cannot... Granted, he did say that after the battery warms up, then the full 16kw would go to the battery. But since they were in the far north, and they were hammering the car during testing, it would not usually send more than 7kW into the battery, since the car would end up sitting in the cold for long stretches.
So with all this being said, I guess my point is that, that you should look at the cost-benefit to all this, becuase it sounds like it's pretty expensive to get a DC charger setup at home, but it won't actually charge your car that much faster than a regular L2 charger.