Want a mechanics input... well here it is anyway!

Heat shields are there to protect things surrounding that super-hot exhaust pipe! It's fine moving down the road with air rushing by, but when a vehicle gets shut down with a super-heated exhaust, the heat rises and super-heats your floorboards and other bits that are nearby that don't take well to repeated, intense, heat!

It's best to try to keep them on.
If they're rattling, any competent muffler shop's welder-on-duty should be able to tack weld them back in place.

...and there's me 2 cents.