Having watched the clip in the OP, I gather that it wasn’t an Aaron Sorkin script?
Hey OP that’s my car! 
How about The French Connection (1971)?
Bullitt was far from your average American cop movie. Firstly it was shot almost completely on location in San Francisco giving it a very authentic feeling. Secondly it had a Euro producer and director which gave it a cosmopolitan flair. Thirdly Bullits wife Jackie Bisset is given agency as his wife. She is an architect. A couple poignant scenes between the two added a depth to the film that was very rare at the time.
That Bullitt chase ended in Brisbane CA, just south of The City. I loved finding the streets of that chase years ago.
Bullitt and Le Mans (another “car chase” film) are both virtually silent films. There are long stretches with no dialog at all, and others with very little. They are almost zen meditative.
Also Bullitt has two chases of note: the footchase around the airport is almost as long and almost as suspensful as the car chase.
Yes the Mustang had a major weight advantage over the Charger but there’s no way way in hell a stock 390 Mustang would run in the high 13s. Low 15’s, maybe squeak into the high 14s with a good launch and the later iteration with 335 HP. The weight advantage would be mitigated by the massive FE engine anyway; Fucking thing is as big as a diesel. Very nose heavy…plowing understeer. 428 versions had the power, but the 390 didn’t and yet had the bulk and weight of the old FE block.
Watching the Bullitt scene again, and it’s been many years, I’m reminded of how the locations and directions the cars are going don’t make sense geographically. But only if you know The City. Otherwise it don’t matter.
Smokey And The Bandit
None of the regular traffic on the roads have any respect for cops running with lights and sirens. Forget The Bandit. They could have balanced the county budget writing tickets for everyone else out there. Well, as soon as they got them to pull the hell over.
And the motorcycle cop never gives Jerry Reed his license back before taking off after the Trans-Am. He’d be busted.
But other than that, it’s damn near a documentary. 
And the short but intense chase in the hospital. What an amazingly filmed scene.
I’m impressed that drivers involved in daredevil chases (protagonists and innocents) have the ability and presence of mind to flick their headlights on and off in warning, as if that’ll do much good.
Here ya go, for non-SFOizens.
Likewise, I defy anybody who has ever lived or worked in Long Beach/South Bay to watch any of the chase scenes in the Nicholas Cage version of Gone in 60 Seconds without yelling “What the Fuck?” at the screen at least a dozen times.
Or the foot chase in Lethal Weapon, where they start out in Reseda and end up on Sunset.
Not really a chase, but in The Bedroom Window a suspect is being tailed through Baltimore and goes the wrong way down two One Way streets, makes an illegal left turn that would have gotten him killed and pulls up in front of a bar that does not exist in a part of town that has no bars.
Plus, the statue of George Washington in the opening shot is facing the wrong way. That’s Charm City for ya.
Except for the fact you can drive from Atlanta to Texarkana in about 12 hours at 55. Even with loading the truck and pee stops it’s no problem to get there and back under 28 hours without speeding.
They also have Bandit near Fayetteville, which is hundreds of miles in the wrong direction. And they have I-95 in the wrong place and wrong direction. All easily fixable errors.
Another in my long-running complaint that Hollywood filmmakers never looked at a map in their lives. Bullitt IS a SF travel map compared to SatB. 
This scene from French Connection is actually my personal favorite car chase scene because it feels real and gritty. It also to my knowledge was shot without permits, so they had to film it over 5 weeks taking time whenever they could around New York’s rush hour traffic to get scenes in. (Despite persistent rumors the scene with the baby buggy was 100% staged and was not, actually a real baby that Hackman had to swerve to avoid.)
How many people even know there was an earlier version? I saw it at the time, but that was many moons ago; I wonder how well it’s held up.
The same stunt driver performed in both Bullitt and the FC.
One reason the older car chases are better than the newer ones is that the stunts are actually being performed by humans instead of CGI. In Bullitt, the Charger was driven by Bill Hickman a legendary stunt driver. His in movie partner was in the passenger seat. During some of the hairier moments in the chase the passenger has visible moments of fear. This was not acting. The actor was scared as shit at Hickmans driving.
The original Gone in 60 Minutes (1974) is on Amazon streaming and well worth the $2.95 rental. The acting wasn’t going to win any Oscars and its moral compass is squirrelly, but, damn, what a great flick! The first half is a master class in auto theft and the second half is probably the most exciting car chase I’ve ever seen on film. And the chase is 40 minutes long! Eleanor and her driver take a bit more abuse than might be believable, but everything else about it is quite realistic. Unlike most chases, it makes complete geographical sense and even shows the kind of collateral damage to innocent people that a real chase would cause.