My house is built in the 1950s. It has a craw space. The exterior
stucco goes all the way down to the dirt, covering the foundation.

Yep, thats bad

On newer constructions, part of the foundation is exposed all around
on the outside, presumably to guard against termites,etc.

Thats the Code now, and for the reason you state.

I am thinking about doing some work on the stucco so part of the
foundation is exposed. Like cutting away the bottom X inches of the
stucco.

Thats a good idea but generally the stucco usually only overlaps the
concrete foundation by an inch or so, just covering the bottom (lumber)
"plate".
The rest of the stucco is generally applied over the plate and wood
sheathing attached to timber studs or 'foam board' over studs. You cant
cut back the stucco there or the inner construction of the wall will be
exposed.

This doesn't apply IF your home is CBS.

Is there any way to drop the ground level a few inches, maybe by grading
away, without creating a slope toward the house ?