In a corporate lab we would use bunsen burners just to ignite the alcohol on a glass spreader before spreading transformed bacteria. I was never a fan of the wire loops, but those would work too since they can cool quickly.

I have never heard a claim that the flame itself sterilized the broader area.

I also used the burner to make the spreaders by melting glass rods to have a triangle-shaped head. Those were fun times.

Edit: We also used to flame the head and necks of a flask before putting a sterile pipette inside. I guess that was to kill bugs lingering on the outside surfaces near the opening.