I can only say that you've completely misunderstood mens rea and must have ignored the links I provided. No, mens rea is not a lower bar than "intent" in colloquial language, and it is not about just actions and not outcomes, else how could anyone commit intentional murder? That is covered in mens rea by the concept of specific intent and general intent.

The usual split in levels of intent depend on jurisdiction but this is a good summary from Wikipedia on the (general) US system application of mens rea that is easy for me to paste, so:

Negligently: a "reasonable person" ought to be aware of a "substantial and unjustifiable risk" that is a "gross deviation" from a normal standard of care.

Recklessly: the actor "consciously disregards a substantial and unjustifiable risk" in "gross deviation" from a normal standard of care.

Knowingly: the actor is "practically certain" that his conduct will lead to the result, or is aware to a high probability that his conduct is of a prohibited nature, or is aware to a high probability that the attendant circumstances exist.

Purposefully: the actor consciously engages in conduct and "desires" the result. The Supreme Court has not found a large difference between purposeful and knowing conduct, not only in theory but also in application.

Drunk driving is reckless behaviour for anyone who knows what being drunk is.

Getting into your car and driving while you're drunk IS creating grave risk to life.

I can't go shooting cans in my backyard and pretend I'm not risking my neighbors lives.