In UK flare pilot.
Mate of mine flies 74's for BA and I'm sure he hand flies every third approach, which for him is probably once a month. Don't know anything about BA but I got the impression it was company policy.
As for your Piper turbo pilot I find it worrying that SEP's are getting to the same level of sophistication as airliners. Guys go on courses to learn the ins and outs of Garmin 1000's etc. At the end of the day it's an SEP, keep your eyes out of the cockpit where they belong and fly the bloody aeroplane, it's not an Airbus. Having said that there have been the odd occassions where I would have welcomed a simple course hold autopilot, not because the a/c is getting ahead of me in foul weather but it just frees up a bit of capacity that you may need.
Don't know how old you are but do you remember when we all magically managed without mobile phones? Now if I get down the road and mrs thing has forgotten hers we have to go back for it. Same with tech, soon guys won't get into their Saratoga or whatever without a GPS or synthetic vision etc. They still crash. Mainly because the warm and safe feeling that all of this tech gives them removes them from the fact that they are flying two tons of metal at 150 kts through the air, relying on nothing more than physics and a single propellor and engine to keep them alive.