I thought exactly the same thing. Peltier's themselves don't really have a pathway for becoming as efficient as steam turbines but there are other methods currently in research.
One promising idea is to use sodium vapor in a fuel cell style device:
http://dx.doi.org/10.1016/j.jpowsour.2017.10.022
The maximum COP for a peltier device is 1, in practice it’s far below that.
Heat pumps go way beyond a COP of 1; an open-loop cooling system with an evaporative cooling tower can have a COP of 7. A closed loop heat pump alone can have a COP of 4.
Peltier devices are a dead end for moving heat around outside of specialized applications where you can’t drag around two heat exchangers, a valve, and a pump (like active cooling clothing). It’s impossible for them to even approach the efficiency of resistive heating (COP of 1).
We need better peltier devices.