It does. Heat conduction is faster when the temperature difference is large. Air soaks up a lot of heat, so still air is a poor heat conductor. If you're blowing it around, you're increasing the amount of fresh, colder air that can interact with the food.
One spoonful and a couple of breaths is small enough stuff to have a relatively small effect and a lot of error margin, though.
Using the phrase "begs the question" to mean "raises the question" is a common misuse of the term. In academic and professional writing, "begs the question" actually refers to a logical fallacy where a statement assumes the truth of the conclusion it is attempting to prove. To avoid confusion, it's best to use "raises the question" when you want to indicate that something prompts or suggests a question.
An example:
"Vintage furniture is better than new furniture because it’s usually made from real wood."
This statement relies on the assumption that real wood is the superior material for furniture. However, nothing in this claim explains why that’s the case, so it begs the question, “What makes real wood better than other materials?”
I don't understand the Mike Tyson reference though.
It does, though. In fact, that's considered the primary definition, per Merriam-Webster.
Begging the question means "to elicit a specific question as a reaction or response," and can often be replaced with "a question that begs to be answered." However, a lesser used and more formal definition is "to ignore a question under the assumption it has already been answered." The phrase itself comes from a translation of an Aristotelian phrase rendered as "beg the question" but meaning "assume the conclusion."
That's a case of a dictionary caving to a misuse being so common that it becomes the new norm. If a dictionary claimed "supposively" was an acceptable spelling of supposedly, would that make it correct?
Besides evaporation, blowing on something which is very hot will bring it closer to room (or breath) temperature by removing the air right next to it which has been heated up already and is 'protecting' the hot item a bit from direct exposure to the room air. When you blow that hot air away the hot item then touches the room air and heats that up, which cools it down.
The same applies to cold things, you can melt ice cream for example much faster by blowing on it even if you use a fan instead of hot breath.
The simple answer is that it takes time. You've removed it from the hot pile of food and given it a few moments to cool, surrounded by cooler air.
I bet if you did an experiment where you blow on on spoonful while it waits and with the next one you just pause without the blowing, you'd find little difference between the two experiences.
You know how you wind can make you feel pretty cold even when it's warm outside? The effect is even stronger for food, since the ratio of surface area to volume is bigger, and the temperature difference is much bigger.