I was wondering: why not take a home equity to pay off mortgage?

We have a $ 200,000 mortgage on a house that is worth $ 300,000.
I was thinking about refinancing, but noticed that a home equity line has a lower interest rates APR.
If I take the equity line and pull out the full amount they will give me (the bank told me it is up to 80% of the value of the house) and turn around and pay off the mortgage, wouldn’t that be cheaper for me ?
Where is the caviot in this theory?

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