I don't have any personal experience with the "flame thrower" types charcoal starters so this may not apply to them, but if you are striking a match for paper towel with oil, or paraffin cubes, or alcohol you may be looking for a way to get that fire going a little faster. The best tool that I have found for this is a hair dryer. Once the flames die out blast the pile of glowing lump with the dryer from the the grill area or shoot it in the bottom vent. In a minute or two you have a beautiful bed of coals. You only need the fan function, not the heat so a broken one with no working heat element is perfect.
A good source of cheap hairdryers is Goodwill or other second-hand type shops. The only problem is that if it is broken with no heat they may throw it away before you get there since "who would want that?"
Mine is always near at hand when I light up.