If the application of carb-heat cannot cause carb icing (and I am not saying that it does) then why is "Carb Heat Cold" included in the cause of engine failure checks, prior to attempting a re-start if the situation will allow?

Because applying power with carb heat on can cause a rich cut.

This is why you should never leave carb heat on, and, saving the blushes of earlier posters here who have mentioned their bad habits in this regard, especially not when a go-around is likely.

To carry out an in-flight restart, you have to juggle the throttle lever. This injects fuel. See my first paragraph. It will be far less likely to restart with carb heat on. If possible, it will take significantly longer. In a light single, time is of the essence if you are restarting. You are using up time with both hands off the column/stick that could be spent setting yourself up for a nice, leisurely forced landing into a field somewhere.