I disagree. You're assuming that only direct punishment can affect behavior, when the _threat_ of punishment after first offense can also affect behavior.

As a ridiculous hyperbole: assume a life in prison minimum sentence is established for speeding, on the first offense, and that it's actually enforced. I guarantee you that very quickly we'd have everyone driving under the posted speed limit at all times.

You're assuming offenders anticipate the bad things they do drunk and thus can be deterred.

Counterpoint to your ridiculous hyperbole: Why isn't the murder rate near zero in states with the death penalty?

Isn't that backwards? If most offenses are first offenses, then firing after a first offense won't help much. But if most offense are repeat, firing after the first offense would have prevented the repeat, right?

What you're saying and what I said are consistent, not backwards.

"If most offenses are first offenses" satisfies the predicate "Unless [% of first offenses] is a really low number"

The consequent "firing after a first offense won't help much" is consistent with "firing after first offense won't reduce the total number of incidents enough."