This is a good illustration of the Golden Rule: "Who ever has the Gold makes the rules."
The bank is not going to give you an inflated "cash out" loan, just because an appraiser says it is worth more than it cost to build. That's how we got into this economic mess in the first place. In most cases, they agree to pay the construction cost UP TO appraised value. If you over-improve the house, they won't likely lend you more than the appraised value either.
If they lend you more than it cost to build it, you reduce your equity, your loan to value ratio increases, which increases the lender's risk.