Smart thermostats need some sort of power. Many get that from the use of batteries. Some of the newer ones tend to use more power than batteries can readily supply, at least with a decent life, without replacement. A thermostat is basically just a fairly simple switch, and just like your wall switch to turn a light on/off, doesn't need power to make it function - temperature makes the switch open/close in a really simple one (electronic ones may use a solid state temperature sensor, but that takes power). A WiFi enabled thermostat usually will need additional power than what a battery can provide. To have useable power at the thermostat, you need the common to complete the circuit. There are ways to siphon off a bit of power on some designs without the common, but you can't get a lot that way. For the HVAC functionality, power comes in, goes to the various switches, and when one or more of them turns on, it sends it back to the HVAC system where it then activates something, completing the circuit. Without common wire at the thermostat, there's no complete circuit to power the electronics of the thermostat unless it was designed with batteries or to parasitically get some while supplying power to something in the HVAC system.