To go into a full development cycle for a new airframe able to lift these bigger, rounder engines clear of the ground whilst still keeping the door heights the same would have taken many years and billions of dollars
Boeing wanted to design a brand-new replacement for the 737 (without keeping the door heights the same, as times have changed and that's no longer of any real value), but when they pitched it (pun intended) to airlines, they heard that the airlines wanted better 737s, not a replacement. While the original 737 design was definitely showing its age, airlines perceived it as working well, and pilots knew how to fly them. It was the airlines that pressured Boeing to deliver a plane with the same type rating as their existing 737s, so no expensive pilot retraining would be necessary, and Boeing tried to give them what they wanted. And then when the new iteration of the A32x series, that just solidified Boeing's plan to refit the 737 once again, which could be done much faster than designing an all-new plane.
I don't think there is any reason to believe that if Boeing had designed the Max to be a new(ish) product that had its own handling characteristics, this whole MCAS thing would not have happened. Trying to cram the new(ish) plane into the existing 737 NG type certification was the problem. It does not handle like previous 737s because it is not one of the previous 737s! It should have had its own type rating, but if it had, that would have erased most of the reason airlines wanted another 737 rather than a clean-sheet replacement.