It seems there is a slight misinterpretation in terms here.
Readers Digest version:
Rc, Rh, R... all the same from a power standpoint, all good for powering the stat. C is the common/ground/neutral, and it is needed to complete the circuit; without it the stat will not "see" power. Power needs somewhere to go, and C completes the circuit. Connecting R (hot) to C (common) is fundamentally incorrect.
Thermostats, in their simpliest forms, are nothing but switches. Switches don't need power. A simple heat thermostat has an "R" terminal and a "W" terminal. R = power, W = heat. When the switch is open (i.e., no call for heat), you can measure 24VAC between R and W. When the switch closes (i.e., call for heat) the circuit closes and there is 0VAC between R and W.
Enter the early programmable thermostat. It had a mechanical clock, and that clock needed power. Conveniently, the clock can "steal" power from the system, but only when there is no call for heat Remember, once the switch closes, there is no longer voltage available at the stat. Manufacturers installed rechargable batteries to carry the clock during on cycles, then the batteries would recharge during off cycles. It worked fine this way for decades, as the venerable
Honeywell T-8082 demonstrated.
Now that mercury switches and mechanical clocks are sitting beside carburetors and rotary telephones in museums, thermostats are moving towards system power to maintain their WiFi and other internal circuitry. In order to provide power to the thermostat during both off and on cycles, you must have the "other" side of the transformer (C) present.
Batteries are still in place but are primarily to provide power for memory during power outages.
Run a 7 conductor bundle and be done with it.
FWIW, my Ecobee runs off 4 wires between the panel and the stat. 2 are DC communication lines and 2 are 24VAC. It also requires complete wiring between the control panel and the system. It's a truly advanced control system, and with it's recent integration with IFTTT, I expect it wil grab the lions share of the market.