The B737NG has high approach speeds because with a long fuselage and low landing gear, pitch attitude is limited so gaining lift through a higher angle of attack isn't possible, the airspeed needs to be kept up.
There is no doubt that a clean sheet design would have been a better option to replace the B737-200, reasons why this wasn't done have been stated above. The 1950s fuselage has always been the limiting factor of the B737. Airbus got it right with the A320 which was designed with higher bypass engines in mind and is able to accommodate baggage containers in the hold, passenger comfort is better and even the amount of overhead locker space is much greater which suits low cost operators with short turn around times and pax carrying more hand luggage.
Airlines such as Southwest and Ryanair are locked into the B737 just like a bad marriage where getting divorced is too hard.