Considering that driving (at least in the US) is a relatively unsafe means of travel compared to the alternatives, I can understand imploring someone to drive safe.

Not just the US.

Rather strangely when choosing transportation options, people generally don't say "I'll take the subway it's safer", when it very much is.

On the other hand people accept things like "I have a fear of flying" much more easily than "I have a fear of cars".