This is likely to also be the only solution for truly 3D integrated circuits (i.e. of unlimited thickness), but it is very difficult to ensure that such a solution has high reliability, because at least for now it cannot be self-repairable, like living tissues, so the cooling network can become clogged or it can start leaking.
This is why a brain or a muscle can scale from a mite with a volume of one thousandth of cubic millimeter to a whale.
The scaling is not ideal because the smallest capillaries must be aggregated into vessels of increasing size, so some part of the volume becomes wasted, but still the ratio of area per volume does not decrease linearly, as in the case when the external surface is used for cooling.
The same technique is applied in many engineering domains. For instance, the maximum current for a power transistor depends on the perimeter of the source or emitter, not on the die area. Therefore, if one would scale a power transistor maintaining geometric similarity, the switched power per die area would drop quickly, leading to very high costs for the devices.
Instead of this, a bigger power transistor does not have bigger sources or emitters, but it has more of them, with the same size as in the smallest transistors, which keeps constant the power switched per die area.
Perhaps a good coolant with a good flow speed can gain you a decent constant factor versus a classical heat sink, but once the third dimension of your chip gets bigger, you will hit a barrier. Just do the math.
Going to keep thinking about this. Could adding an impossible dimension be Triz 41? Maybe when we get to Triz 42 we'll figure out how to stop fighting over meaningless stuff as a species.
Edit: It's actually just Triz 17(another dimension)
I am not sure where am I going with this, but it would be funny to have chips with big ears and a fake mustache.