A video about Cole-TAC suppressor covers touts the fact that they can be tightened enough to prevent their moving forward due to recoil. The concern the narrator expressed was that if the cover moves forward it can act as a muzzle “crown” that disrupts the even expansion of the gas as it leaves the suppressor. That in turn can supposedly affect the bullet and the precision of the shot.

That claim seems doubtful at best to me, not least because high speed videos of shots from suppressors seem to indicate that the bullet has left the can far behind before the gas expands enough to reach the cover even if it were extended beyond the front of the suppressor.

But I’ve been wrong before, so what say the people who really know? If a suppressor cover extends past the front of the device, can that have an effect on the precision and accuracy of a shot?

A suppressor cover that extends an inch or two forward of the (can's) muzzle doesn't seem to affect accuracy or POI. I've seen this multiple times with other shooters in competition, and even a few times with my own rifles.

If the suppressor cover slips forward more than a few inches, there is a good chance that it will droop into the bullet's trajectory. I've seen this happen a couple of times. This doesn't bode well for both the bullet's POI and the cover's future utility.

Most of the problems I see with suppressor covers is from cans that have sideways vents on the forward end of the can. I assume such vents act as a brake of sorts -- and this type of can isn't very quiet. With vented gas going sideways from the muzzle, if the suppressor cover gets too close to these vents, the front end of the suppressor cover gets shredded.

All right; thanks for that.
The cover I have is constricted at the rear so that it cannot move forward, but I was curious about the value of an extremely tight fastening system that the one company touts.