Why aren't CPUs cooled from below as well as above?
They aren't cooled from below because they have pins on the bottom, and FR4 below that.

Due to having a much lower thermal conductivity,
$$
\begin{array}{rrl}
\text{Copper:} &amp; 385\phantom{.25} &amp; \frac{\mathrm{W}}{\mathrm{m}{\cdot}\mathrm{K}}  \\
\text{Aluminum:} &amp; 205\phantom{.25} &amp; \frac{\mathrm{W}}{\mathrm{m}{\cdot}\mathrm{K}} \\
\text{FR4:} &amp; 0.25 &amp; \frac{\mathrm{W}}{\mathrm{m}{\cdot}\mathrm{K}} \\
\end{array}
$$the material on the bottom of the CPU would transport much less heat.

Odds are you wouldn't want to surround the signals with metal which would change the impedance drastically, so metal on the bottom is more of an issue. If you did build a socket out of metal, it would need to be micromachined, which would be many times more expensive than a plastic injection molded socket. These things would prevent you building a processor socket that would wick heat away.

You could put a cooling block on the bottom of the board, but the PCB material (FR4) would reduce the cooling substantially.