There is no provable benefit to having a parallel section nearest to the muzzle. This has been argued, tried, abandoned and retried for ever and ever. It also doesn't necessarily hurt patterns any. At least one of the aftermarket choke tube manufacturers today touts it.
Great patterns are shot with chokes that have, and have not, the parallel section. There is no shortage of folks with "new ideas" for choke profiles. Check out the Brain Chokes:
https://brainchokes.com/inner-profile/ As to a parallel section preventing flyers ........ I don't agree with that postulation. Flyers are misshapen pellets, which are caused mostly by setback (upon ignition). The only way I am aware of to help alleviate this problem is by using harder shot. Prior to plastic cushion wads flyers were often caused by bore scrubbing, too. Not so much with modern cushion petal wads.
Choke profiles are interesting, but no one profile yet has taken the shotgunning world by storm. Again, great patterns are where you find them, and they can be delivered from many different choke profiles. The AH Fox HE grade (SuperFox) was developed to deliver the tightest and finest patterns with Olin's new SuperX Luballoy load. Much r & d time was spent doing this. What emerged was a constant taper, beginning some 4 inches back, all the way to the muzzle, with no parallel section. LC Smiths, OTOH, were bored with a parallel section. You paid your money and you took your chances.
JMO,YMMV
