This is most likely a restriction of the used signalling protocol. As mentioned on Wikipedia's CCS: Charging communication:
AC charging is possible using the PWM signal only. In this case the charging station uses the duty cycle of the PWM to inform the onboard charger of the maximum available current at the charging station (A pulse width of 5% indicates that HLC shall be used).
It should be noted that the signaling protocol in IEC-61851 is copied from SAE J1772 which encodes the maximum charging current on a PWM signal of "1 kHz square wave on the control pilot". It has a ratio of 0.6 A / 1% of duty cycle. This makes 6A equal a duty cycle of 10%. It's likely that a combination of wanting to have decent signal/noise resistance in the beginning, and now, having some headroom between the 5% duty cycle indicating HLC, lead to a 10% minimum.
Maybe the HLC protocol provides some further provision for limiting the current further than 6A. But you wouldn't be able to rely on it (for now) because HLC itself is an extension that may not be implemented by your car.
Also: it's perfectly possible to charge at less than 4 kW still: you don't need to charge on all phases. 1 phase leads to a power limit of 1.38 kW. In fact a lot of EVs only have a single phase onboard charger. Often you can recognize this by the absence of metal in the L2/L3 pins of the female (type 2) socket on the car.
My car is one of those restricted to 1 phase, and when charging from my solar panels I almost always have it restricted to 6A. It usually stays a bit lower at 1.3 kW. A neighbor's car does have the ability to charge at 3 phases, but he still only charges it with 1 (though he goes for the full 13A his circuit can provide).