I don't think it would be as simple as a high heating bill. A residential furnace is certainly not made to run 24/7. No big deal if you're at work but if you're out of town for a while...
The thermostat doesn't actually control the plant directly. It requests heat or AC by closing a connection. The HVAC controller responds to those requests as it is able to as per its programmed parameters.
You're absolutely right that furnaces aren't designed to run 24/7. But your thermostat can request heat 24/7 and unless the furnace control board is broken, it'll the cycle the system as necessary to keep up with the requests.
Most people never learn this because the systems are designed for peak needs and most days don't get anywhere near peak.
> But your thermostat can request heat 24/7 and unless the furnace control board is broken, it'll the cycle the system as necessary to keep up with the requests.
I have a hot water boiler. Even when constantly calling for heat, I can hear the element relays click on and off to avoid over-pressuring. The recirculation pump stays on the whole time.
(I'm agreeing with you; just pointing out that my system does cut out under normal operation, while calling for heat.)
