This is a very good question, and I don't believe there is one answer that fits all scenarios. For instance, an existing condo will be fairly standard in requirements for a lenders approval, such as a percentage, usually 60-70%, of owner occupied units for a buyer to acquire financing.
New construction and condo conversions, however, have a few more requirements for approval. One lender I have been working with on a condo conversion I am doing now has agreed to finance buyers once we have two "pre-sold" units. This lender will approve the building in advance of the buyers coming in, and will then review each buyer individually and provide loans for that buyer to choose from based on their specific needs. If that same buyer went to a lender who hasn't preapproved the building in advance, that lender might not fund the loan for the buyer and unfortunately, this happens all too often.
While I agree that all good faith estimates, rates and fees should be checked by other professionals in that field, there is a reason for preferred lenders and if the buyer finds the rates and fees don't match what they are hoping to find, the condo/new construction home might not be the right one for them.
Having said this i do believe that new construction single family residences are much more liberal in terms of lender requirements, and the buyer has much more latitude when it comes to making their lender selection.