Preponderance of the evidence is the legal yardstick for all civil offenses, everywhere in the US, as far as I know. This translates to "more likely than not." Beyond a reasonable doubt is only used for crimes, I think. Traffic law enforcement would be basically impossible if this standard were used.
Speed is a real thing, as we know. 60 mph is 80 ft/sec. When three tons are moving that fast, we have what is called "inertia."

In my view, people who follow less than one vehicle length behind another car at 70 mph just simply DO NOT UNDERSTAND physics and should not be operating a motor vehicle.
But I agree with Jeff here. Again. I have loved the art of driving since before I got my license. I know where the other vehicles are, at all times. I watch them. I have an escape plan, always. I leave responsible following distances. I avoid stupid people. There are a LOT of stupid people. A LOT.
And I exceed the speed limit almost always.
Our state patrol used to cite motorists on only 30% of stops. On all stops, they tried to educate. Their goal was public safety. This does not seem to be their goal now. When a brake light or tail light goes out on a car that only has two, then that car is only one small filament away from having none. Brake and tail lights are a redundancy. If law enforcement were to return to a public safety goal, then tickets would be issued for non-speeding stuff that is dangerous. Rules would be followed. Motorists would be educated, and this would help make their driving decisions more predictable.
Our public roads are a friggin' free-for-all. A great many drivers are failing to follow the rules. We all depend, for our safety, on the behavior of others. Not following basic traffic rules is dangerous. It means we never know what that other driver is going to do. Surprises everywhere. It's scary. I really don't like to drive much these days. Every time I go out, I see VERY stupid decisions being made.
I do have what I feel is a good idea for revenue that could help support law enforcement and/or transportation infrastructure: When I was commuting Auburn to Lynnwood and back each week day, I payed attention to what proportion of vehicles used the HOV lane with no passenger. About 30%. This made sense to them. The likelihood of getting caught was low. The fine is not expensive when you consider it to be a fee to use the HOV lane and save yourself several hours a week. While I recognize and understand this logic, I think those people are thieves. They think they are clever. I think they are dishonest cheaters. They are making a conscious decision to take something, unlawfully, that does not belong to them. They see law-abiding citizens as "suckers."
I think the fine for HOV violations should be $5000. In all those cases, LE could meet the "beyond a reasonable doubt" standard of evidence. Either there is one person in the car or there is more than one. Integer math. I wish they would do this. I hate bullies and I hate cheaters. Those behaviors should be painful.