This might have got lost in translation.What Otter meant to express ist that the space inbetween the windings - not the space from winding to winding, but in the middle of teh corkscrew - is there to prevent crumbling.In german it´s called "Seele", soul in english. Something that is not there but serves a purpose.On older and cheaper knives you often see a corkscrew that looks like a screw with a coarse thread or a big wood drill bit. Those do not have a core or soul. As they displace more room, they sometimes make the cork crumble.I hope I did explain that well enough in school learned english...
I suspect the flute was nothing more than a residual line after it was swaged from a stamped plate to a rounded section. No function. No decoration. Just a residual feature of the process.
All the better corkscrews have that line. It gives extra grip, reducing the chances of the cork screw getting pulled through the cork and creating a great crumbling mess. https://www.johnlewis.com/le-creuset-wine-accessories-waiter%27s-friend-bottle-opener-wood/p231329768?sku=231329768&s_kwcid=2dx92700040042509457&tmad=c&tmcampid=2&gclid=EAIaIQobChMImceU3IuP4QIVAZztCh35lQ_sEAQYByABEgILuPD_BwE&gclsrc=aw.ds
1. After some consideration, I am of the opinion that a properly cut groove in a corkscrew (especially a corkscrew made of questionable steel and with questionable or no heat treat) might serve to stiffen a corkscrew
2. Using modern steel with modern heat treat, however, resulted in corkscrews that were plenty stiff without the groove, and since the groove was an added cost, it was ultimately dropped. It seems likely that the grooved corkscrews continued to be used long after any actual benefit had disappeared due to public opinion (i.e. people believing that quality corkscrews had grooves) and or tradition.