What about HBM on the back side of the chip ? Essentially I'm thinking like a soldered on piece or another "socket" with pins like a CPU in the back of the motherboard. We rare see cooling elements there already and while most rack mount cases are not at all designed for more space there I don't see why it couldn't be a thing. Especially with liquid cooling.
Also makes me think of possibly using Gallium Nitride instead of silicone for surface levels elements ? Or maybe even an interface layer on top or bottom of the chip designed to be able to transmit power with less heat. Maybe that could be sandwiched between the chip and HBM.
I think the switch to GaN is already happening for power, but Si is considered better for logic dies like the GPU. Also GaN is worse thermally than Si so the problems are actually amplified