I have only ever sceen the round ones that cover the burners.
I have never seen one that covers the whole surface, but it seems practice - it creates more counter space when you are not using the stove to cook (which might be a lot in a hot climate).
My stove has a solid piece of tempered glass covering the whole top - the burners are hidden beneath (the glass is very dark, almost black). It is supposed to be easier to clean.
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ADHD-I(diagnosed) ASD-HF(diagnosed)
RDOS scores - Aspie score 131/200 - neurotypical score 69/200 - very likely Aspie