Orbital datacenters suffer from the same problem: limited surface area. You think cooling is a problem now? Try not having conduction or convection. Radiation is all you get. A huge proportion of the mass and size of the ISS is radiators, and that only has to deal with the heat of low-power electronics and a few measly human beings.

Using an entire Mars only nets us about a 2x multiplier for our energy expenditure budget. Then we need four planets to double it again. Exponential growth is a bitch.

Thermodynamics and the tyranny of exponential growth are going to win this battle every time, regardless of the unobtanium technology you try to invent.