What incentive does the lender have? The involved parties are the seller, the buyer, their agents, and the originator of the loan. All of these people are working to close the deal at the negotiated price. The originator of the loan will hold the loan for somewhere between 72 hours and 30 days, so they don't care.
Of course they care; any money they give you over the value of the home is unsecured! They're not going to lend you e.g. 20k @ 3.5% with no collateral. C'mon.