the oh-so-pilot-friendly-and-simple-and-manual 737 doesn't pass pitch stability certification criteria
Maybe the 737-100 did pass the criteria of the 60s... At least for gliders I definitely know that the required stick forces were increased in the late 70s, so the earlier ones had significantly lower stick force gradients than current types. Same may be true for transport aircraft, so maybe boeing added this feature for the NG... Maybe even voluntarily, to meet the latest standards.
Why would they authorise aircraft clearance to fly when the problem never went away after fitting the new sensor .
Well, the just learned during flight that the problem was not solved... Normal for issues not reproducible on ground. You troubleshoot per the manual and see whether the problem is solved during the next flight.