I think there is a little misunderstanding by some who have posted referring to just a plug or just a patch. The OP is referring to a plug patch combo which is like a flat headed mush room. There are 3 ways to repair a tire. With a plug. With a patch. With a one piece plug patch.
Personally all but one of my repairs has been with a patch. The one time a plug patch was used was at the recommendation by the tire tech since the hole was made by a 3/8 inch bolt instead of smaller screw or nail. The hole was already punched wide through the steel belts and the plug patch was needed fill up the large hole made. The tire was fine afterwards until it needed normal replacing due to the treads eventually wearing away.