Blackmail ,the new procedures on the 737 does not affect the QRH,and in no way there is a reduction of the items required to complete a malfunction using the qrh.
Those procedures changed mostly the areas of responsability for both pilots,during different phases of flight.The items that existed before,are still there,but in some cases must be done by the other pilot than before.
The checklists does not require the backup of the ecam,actually,for the qrh,the ecam replaces the standard qrh book.
The QRH is very good on the 737,but ,like the ecam ,does not cover all the possible situations and multiple faults.Mostly on multiple failures,you have to know the systems,and use good judgment.The same is valid for the ecam,proved more than once on the bus ,for ex.
Why do you think there is no ecam on the 737? I think for commonality between dif series,as we know that the 737 dates long before the ecam..till 2005 the 737 did 76 milion flights compared for ex,with the 6 milion flights done by the A320 family (newer plane,state of the art ecam ). Considering there are still -200 flying,you have the reason for the ecam not being there. I wonder if the NG is ecam capable,if desired by any customer?