On Tue, 7 Feb 2017, Jeff Liebermann wrote:

On Tue, 7 Feb 2017 09:40:24 -0800 (PST), "
wrote:

As it applies to two-wire heat-only stats:

If a digital thermostat only had to run a furnace, life would be easy.
However, it's also used for heat pumps, staged HVAC, solar, radiant
(pump with pipes in the floors and walls), exhaust fans, etc. Note
the maze of wires and functions.
https://xtronics.com/wiki/Thermostat_signals_and_wiring.html
However, I think the real reason they run on battery is that batteries
are cheaper and smaller than a regulated, protected, and approved
power supply.

And unless they can get power from the control line to the furnace, it may
not be convenient to have a power supply. There are suggestions on where
to place the thermostat, and there may not be a convenient outlet just
below.

Michael