I think it is important to remember that The Harold was created as a way for Del to get his actors to get away from or to stop relying on plot to create the performance. I don't have a citation for that, but I'm sure I could find one if pushed.
Here is a second-hand quote. It is from Kozlowski's
The Art of Chicago Improvisation, but he is quoting
Truth in Comedy (Close, Halpern, and Johnson):
the group was searching for some way to unite all their games, scenes, and techniques into one format; they developed a way to intertwine scenes, games, monologues, songs and all manner of performing techniques
For the Harold to not be a fossil it should incorporate whatever you have available and what ever the performers think will serve it rightly, in any given moment. The formula (Opening, 3 1st beats, group game etc) is fine and works and can be used to create a great performance. So can the pot luck approach that appears to have been the thing before the formula became formal.
Drilling the Harold over and over in a particular way in a particular style will teach student improvisers (of which I am one, not to sound above the fray) to play in a particular way, not a universal way. While improv is improv and the skills translate from style to style and form to form, the skills needed to do a 25 minute Harold are not the skills needed to do a 40 minute Deconstruction or a Slacker. Drilling in just general scene work and scene structure, to me is more universally useful than drilling any single form.