Yes they will under very specific circumstances pay off the mortgage, but then they essentially will own the property and that is not the business of insurance companies.
This is a standard Homeowner's policy from the CA Dept of Insurance:
Mortgagee interests and obligations
If loss hereunder is made payable, in whole or in part, to a
designated mortgagee not named herein as the insured, such interest
in this policy may be canceled by giving to such mortgagee a 10 days'
written notice of cancellation.
If the insured fails to render proof of loss such mortgagee, upon
notice, shall render proof of loss in the form herein specified
within 60 days thereafter and shall be subject to the provisions
hereof relating to appraisal and time of payment and of bringing
suit. If this company shall claim that no liability existed as to
the mortgagor or owner, it shall, to the extent of payment of loss to
the mortgagee, be subrogated to all the mortgagee's rights of
recovery, but without impairing mortgagee's right to sue; or it may
pay off the mortgage debt and require an assignment thereof and of
the mortgage. Other provisions relating to the interests and
obligations of such mortgagee may be added hereto by agreement in
writing.
Company's options
It shall be optional with this company to take all, or any part,
of the property at the agreed or appraised value, and also to repair,
rebuild or replace the property destroyed or damaged with other of
like kind and quality within a reasonable time, on giving notice of
its intention so to do within 30 days after the receipt of the proof
of loss herein required.
Abandonment
There can be no abandonment to this company of any property.
When loss payable
Except where assessment is required as hereinafter provided, the
amount of loss for which this company may be liable shall be payable
60 days after proof of loss, as herein provided, is received by this
company and ascertainment of the loss is made either by agreement
between the insured and this company expressed in writing or by the
filing with this company of an award as herein provided.http://www.leginfo.ca.gov/cgi-bin/displaycode?section=ins&group=06001-07000&file=6010-6021