1. Since June 1st under the HVCC rules the appraisor cannot be chosen by anyone except the bank making the loan (NOT the Loan Broker). This can now greatly increase both the time to obtain the appraisal, and the accuracy of it. Ask you loan agent to explain the details about this.
2. Most Lenders now do a review of the original value provided by the appraisal, and can and will reduce the amount of your loan if it finds that more recent sales indicate a lower value. This review is the last thing done before final approval of the loan and can blow the deal out of the water. If you had previously removed your Appraisal or Loan Contingencies you stand to lose your escrow deposit.
This is something you need to understand fully before agreeing to remove these contingencies.
Yes 7 days are enough if you have your inspectors lined up to go in right away, and yes the banks get away with it because the way the market is now ( multiple offer situations ) if you want the property you play the game. If it is a good property or a priced right fixer it can be worth the hassel.