Got to walk before you run.
Handflying is absolutely essential to those greater skills and a ridiculous amount of us do not have the simplest feel for the airplanes we fly. And there is no good justification for it.
Wave, I'm a little surprised as a SWA pilot you would be flying with a ridiculous amount of pilots that don't have a feel for the 737?? That should be SWA pilots strength giving the amount of take offs and landings you guys do. You guys spend a career flying one kind of A/C and that should be your strength. Those of us who fly different types of A/C in different types of environments during our careers are the ones who should be especially vigilant to keeping our hand flying skills sharp.
I can tell you from experience that long haul flying is were you really see the importance of staying on top of hand flying skills.
It's not that hard to do, it just takes a conscious effort to practice, as you pointed out with a little hand flying.