You might in a state of nature, but the US has laws against prepayment penalties for mortgages. (Well, against the mortgage originator charging prepayment penalties.) You don't owe interest until it accrues.
Right, you 'owe the full amount of accrued interest'... Which is not as much as the amount that would've accrued if held to term. I think this is rather beside the point anyway!
You might in a state of nature, but the US has laws against prepayment penalties for mortgages. (Well, against the mortgage originator charging prepayment penalties.) You don't owe interest until it accrues.