Seems like a solution that will make more problems. Sounds like the new cooktop uses IR elements which are just fancy resistive elements surrounded by a pretty white ceramic holder and spaced below the top ceramic-glass cooktop by a few inches. The only thing I can see happening is adding a new layer of material to heat will slow cooking, plus the element and parts below will be hotter because of the small gap between the cooktop and protector.
If you have an induction cooktop the use of one increases the space between the magnetic coil and the metal it is trying to heat, more so those elements often have a heat sensor and metal sensor to check that the pot is heating but not overheating, and that there is a suitable metal pot on the cooktop. The increased space could screw with either of them, but its the extra space that will reduce the heating on the pot. From an electrical standpoint I don’t think that would be good for the driving electronics which generate the magnetic field by screwing around with frequency and voltage.
Get a bottle of cleaner for cooktops, is a white creamy stuff that will allow you to remove cooked on stuff and dirt.
Never put a pot lid down on your cooktop, air trapped under the lid will cook and condense and form a vacuum which could shatter the ceramic glass. Also get a can or bottle of barman’s keeper, that stuff is great for cleaning dirt from stainless steel (don’t use this on glass or ceramic as it’s going to dull the finish), clean all the pots and pans you have, that will help cooking off dirt from the pot onto the cooktop.