I’m not sure if you got my point (or perhaps I didn’t get yours 
).
What you suggest works on simple states but in my example above the climate icon should show if the aircon is on or off and yet still show the temperature in the label. Thus needing 2 item states in one section display:
Text item label icon {
…
…
}
At a glance I can see both if aircon is on (icon state) and the inside temp. In one line and not two. With 2 lines it is trivial to do. How to combine the left icon to represent on/off state with the right hand side space to show temperature.
This is extremely useful for at a glance and space saving so I’m surprised more people aren’t asking for this.
Here I found 2 links that discuss something similar but it seems it’s not possible:
Switch, adjust item label depending on current - #7 by rossko57
If the icon has to reflect item state then for on/off I have to use the switch item reference. Now, the label is text/string. Feels odd that this string can’t contain a reference to an external variable (state of a different item eg. temperature)
edit: you did answer ‘yes but not easily’. I would be very grateful if you have suggestions/examples specifically for the on/off and temperature case. I guess I’m not advanced enough yet to extrapolate from the garage door example. 
edit 2: ok I get it now. I was missing that visibility can be applied to sections!