I was also taught to always dock in neutral and use the transmission for occasional speed control.
From reading folks' posts, however, it seems that most places have a different dock setup from many of the marinas around here. Many docks, including mine, have no cleats or pilings, just a 4x4 "rail" running along the length of the dock, bolted in with a gap of about an inch between the dock and the rail. So all these brilliant spring line techniques are for naught.
I leave an after spring line permanently tied to this rail. The loop is on the boat end and the line is just long enough to reach from the end of the dock to my jib sheet winch or cleat. I drift into the slip in neutral, hop off from the shrouds as they pass the end of the dock, and put this line on the winch. It can be done singlehanded.
Fortunately, it's a small boat and I can manhandle it a bit if necessary. For a larger boat, I can see the wisdom of not getting off until the boat is stopped, but for that I'd like to see a system whereby I can easily grab a permanent dockline from the deck.
The other problem, of course, is docking at unfamiliar docks. When visiting a marina, I will often dock not in a slip but in some sort of temporary dock; often fuel docks or guest docks are easier to get into. Then I'll go check out the slip and maybe prep some dock lines for it. Still pretty stressful, though.
1972 Catalina 27