The military/trench gun type heat shields/bayonet lugs were held in place by screws that engaged notches in the barrel, or in the case of the Remington 870 Mk 1 (which had a bayonet lug but no heat shield), the magazine extension. Far as I know, none of the current heat shield offerings have anything to keep them in place save clamps, and I have seen them move around on the gun under recoil enough to cause problems with the function of the gun.
Heat shields make keeping the exterior of the barrel cleaned and oiled more difficult without taking them off and putting them back on.
I've never seen any advantage to having one, and I've done formal shotgun classes and shot 3-gun. But if you like the idea, feel free.
Mindset - Skillset - Toolset. In that order!
Attitude and skill will get you through times of no gear, better than gear will get you through times of no attitude and no skill.