No, you probably don't NEED one.
Statistically speaking that is.
Statistically speaking, armed encounters are fast. Several seconds and over. You likely WILL NOT have time to get back to your vehicle and retrieve a long gun in a typical gun fight. Sure there is the off chance situation where you are in the area of an active shooter and say "shit! I still don't hear sirens and this guy is offing people". It HAS happened. But the odds it'll happen to you are very very slim.
That being said, my work vehicle has a lock box with an 10.5" M4 and Glock 21, and full load out. My personal has an old chest rig, and when I go out of town I usually have a broken down AR in a duffel bag.
The gear in my work car gets used regularly. My personal does not, and probably never will. I recognize that, and if I happen to not have it or take it, I'm not concerned.
I'd argue that you are FAR more likely to need a IFAK/TQs/Fire ext before you need a long gun .
You can argue Kyle Rittenhouse, and I see your point. But he was not just out and about. He went into a WarZone. If I were in his position.....
ETA, really liking that Sig MPX.