" Maai is keeping distance first and foremost."
I always thought Maai is being mindful/aware of distance.....Be interested in the literal translation.
Maai is not just being mindful or aware. It is an actual distance. When someone is outside your maai, they will have to make - and transmit to you - a body movement of some kind - before they can strike you. Inside your maai, they can strike you without making or transmitting any body movement or adjustment. Maai changes depending on what someone attacking would use as a weapon. If it's their hands, that's one distance. A short stick increases maai. A bokken/sword even more. A jo more. A gun.. could be lots more.
So, understanding what those distances (maai) are, with practice, then allows us to learn to be mindful/aware of maai. The awareness of it creates a type of mental-energetic field around nage, in which intent of someone outside of maai can be sensed by nage.
It's like getting used to driving a car. The boundaries of the car are larger than you, but after awhile you get used to accurately judging the position of the body of the car as it moves through space. This then becomes automatic, requiring no effort.
My 2 cents