I'm having a very difficult time finding images of a Formula One car coming to rest inverted following a crash. I'm trying to compare images with and without the Halo device. Here are the best I've come up with, with a little commentary about why I think the Halo had nothing to do with extraction time.
Sergio Perez, Hungary 2015
Clearly the car is listing to one side, allowing Perez to extract himself from the side of the car that is raised up off the ground. The car is leaning because it is actually resting on the top of the air box / roll hoop, a structure which still exists with the Halo in place.
Pedro Diniz, Europe 1999
In this unfortunate case, the roll hoop actually dug a trench in the ground, causing the car to sink deeper than perhaps it would be expected to. Diniz was completely trapped in the car
because of the roll hoop. Hard to say what effect (good or bad) a Halo would have had here.
Pascal Wehrlein, Monaco 2017
Once Jenson Button flipped the Manor onto its side, his momentum further pushed the car into the barriers, top-side first. Wehrlein was trapped in the car because of the soft nature of the barrier collapsing around him, and not because any structure of the car failed. Consider if a Halo were in place here. Remember that drivers are not expected to exit the car through the gap between the Halo and the car, but rather directly through the top of the Halo opening. That opening would still have been blocked by the barriers.
Fernando Alonso, Australia 2016
Alonso's car came to rest neither completely inverted, nor resting against the barriers. There is just enough space for him to squeeze out. Imagining the presence of a Halo in this image, I believe Alonso still could have made it out through the top of the Halo before being trapped by the barrier. If he had come to rest closer to the barrier (or against it like Wehrlein), then extraction would be impossible without uprighting the car, regardless of the presence of the Halo.
Nico Hulkenburg, Abu Dhabi 2018
Just as in Perez's accident in Hungary, Hulkenburg's car came to rest on top of the air box / roll hoop. Unfortunately, though, the rear of the car is resting on the barriers, preventing it from rolling onto one side to provide him a gap through which to crawl out. On top of being inverted like Perez, he has also experienced the helpless entrapment situation like Wehrlein, because the entire exit area of the Halo is blocked by the road surface.
Is this a foolproof analysis? Far from it. I would be flattered if you were to think I did that and still did a poor job of it. I just wanted to provide similar situations from the past, and try to show why I believe the Halo wasn't the problem. I believe it was the type of accident and the final resting position of the car that prevented quick extraction of the driver.