Most of the batteries in use utilize somewhere in the high 300-400 volts fully charged. There are some out now, and probably more coming, that utilize up to 800-volts. So, while I haven't looked, I'm guessing the DC fast charging 'levels' may be tied to the voltages available. A CCS unit is a variable DC power supply, and the different levels may indicate what range of output they can provide...guess I'll look into that before I buy another vehicle that can do CCS charging. I'm selling my i3 and have an X5 PHEV, and it doesn't even have CCS capability. It's unlikely a homeowner in the near term will have a CCS unit in their home because of the cost and power input requirements. The i3 can handle 50Kw input...using a 240vac supply, if you assume 100% efficiency, that's over 208A and more realistically, you'd need closer to 230A input and if you then factored in the 80% rule, over 260A...my condo only has a 100A service! And, not many homes will have nearly 300A spare power coming in, either!
A CCS charge, when you need it, is great, if it works and you can find an open unit. The i3 was designed as a city, commuting vehicle, so a CCS charge, while nice, wasn't considered critical except maybe to those city dwellers that can't plug in when they get home. IMHO, it's not a great long-distance vehicle choice, and that's where CCS charging shines, and becomes almost a necessity. That's one reason why I bought my X5 PHEV...I can go EV mode for most of my driving, but easy, quick refueling along the way should I need or want to go further, even on the spur of the moment.
2014 i3 BEV, 2021 X5 45e
(The i3 will be sold soon, <17K-miles, interested?)