Tesla made some fundamental tradeoffs by the smaller connector. They basically made it so the switching from DC to AC charging has to be done by the charger circuit, since the Tesla pins handle both DC and AC. CCS/J1772 completely separated the pins so you don't have to do any internal switching, you just have the DC charging pins directly connected to the DC circuitry and the AC pins connected to the AC circuitry.
Also, keep in mind Tesla uses the 'Type 2' connector in the EU since they handle 3-phase power. Same compromise as in the US, but it's larger since it has more pins for additional 3-phase power support. The Type 2 connector is larger than the US Tesla charging port.
I believe CCS is also rated for 1000V usage, whereas the Tesla ports are only rated for up to 500V. This has to do with separation distance between the two pins so therefore the CCS is inherently going to be a bigger connector. The Taycan is the first car I think that is supposed to utilize the 1000V, so it actually needs the CCS separation.
If Tesla ever decides to move to a 1000V system (currently they use 500V), then the connector would need to be redesigned. There's not a ton of reasons to actually move to a 1000V system for cars, as far as I can tell. For trucks (semis, etc), the higher voltage could be very useful since you no longer need to use such large connectors. Honesty, it seems to me the 1000V that the Taycan is advertising is mostly marketing than anything else.