I think your reasoning misses the fact that when using the brake all 4 wheels will slow down the car, but when using regen only the rear wheels do.First you don’t want the car to slow down. Now you say you actually had to slow down.
If you had to slow down, and the car couldn’t handle it, while the car in front of you could handle the same amount of deceleration without problems, then it is a clear sign that your tires were not as good as his.
So what would you have done in a car with no engine braking? You can’t avoid hitting the brakes, because then you will hit the car in front. You can’t brake either because we have just established that your tires are not up to it.
You have basically two options until you get better tires: Keep better distance to the cars in front. Or don’t drive.