Occasionally, with the Capt's agreement, I sometimes choose to disconnect at FL100ish and perhaps get the Captain to take the FD off on final. Keeping on top of raw data handling is important as flying is a multi-faceted skill and all areas need regular exercise. However, the most important thing is managing the flight as a whole which really requires automation to keep work load down for both pilots in anything less than excellent VMC and a low traffic environment (as previously mentioned).
Yes, the 737 is very easy to pole around the sky, but if it does get unstable the situation can deteriorate incredibly rapidly!