Actually, yes burn in cover is specifically mentioned as you can see below in an extract from my policy.
Cover for your product, for example, electronic appliances and/or household goods, against accidental damage.
What is insured?
immediate protection of your product from accidental damage (
including TV screen burn)
unlimited repairs on your product (including call-outs, parts and labour), with no excess to pay
a replacement product (for example where we cannot repair it or we decide that it is uneconomical for us to repair your product)
a gift card for the full retail price of a replacement (if we cannot reasonably arrange a replacement)
delivery of your replacement product and replacement TV installation