Probably not, if they're all computer-controlled, and can communicate with each other. I posit traffic jams is mostly caused by idiot and reckless drivers...

Yup, and if every car is computer controlled and in communication with nearby cars you can safely reduce spacing. Most of that space between cars is due to human reaction time. (And even then that's not always enough. 40 years ago, I'm going along, geezer is being awfully slow about their left turn so I lightly apply the brakes. Geezer then proceeds to completely stop, utterly unaware that I'm heading right towards his door. I slam on my brakes. I was able to stop for said geezer but the woman behind me didn't have the usual warning of brake lights flaring and came up a couple of inches short in stopping. Geezer proceeds off, apparently completely unaware of the accident he caused.

(And that was not the only close call I had with that geezer at that corner.)

Most humans don't leave sufficient braking time on crowded roads. They leave almost enough space to stop, not accounting for reaction time at all.

The future where all cars are computer controlled is even further away than the future where fully self-driving cars are available for purchase.

The throughput of a road is car density * speed. So from a pure throughput perspective, the ideal driver is a tailgating speed demon. To maximize time spent at high speed you should also floor it when the light turns green, and slam the brakes at the last possible moment when it goes red.

One thing I forgot to mention, braking as late as possible doesn't help you at all, but it does free up road space behind you, which can let people behind you get through an intersection they otherwise wouldn't.