In my experience neither of your points is true of a modern heat pump nor a modern gas system. All heating systems are generally optimized to bring homes from 1

In my experience neither of your points is true of a modern heat pump nor a modern gas system. All heating systems are generally optimized to bring homes from 16°C to 22°C in about two to three hours. If your heat pump can't do that it's too small (or your radiators are too small). If your gas system can do it in an hour it runs way too hot and you're wasting a lot of gas.